医疗废物和污泥共熔融

Original ArticlePredicting the co-melting temperaturesof municipal solid waste incinerator flyash and sewage sludge ash using greymodel and neural networkTzu-Yi Pai1,Kae-Long Lin2,Je-Lung Shie2,Tien-Chin Chang3andBor-Yann Chen4AbstractA grey model(GM)and an artificial neural network(ANN)were employed to predict co-melting temperature of municipal solid waste incinerator(MSWI)fly ash and sewage sludge ash(SSA)during formation of modified slag.The results indicated that in the aspect of model prediction,the mean absolute percentage error(MAPEs)were between1.69and13.20%when adopting seven different GM(1,N)models.The MAPE were1.59and1.31%when GM(1,1)and rolling grey model(RGM (1,1))were adopted.The MAPEs fell within the range of0.04and0.50%using different types of ANN.In GMs,the MAPE of1.31%was found to be the lowest when using RGM(1,1)to predict co-melting temperature.This value was higher than those of ANN2-1to ANN8-1by1.27,1.25,1.24,1.18,1.16,1.14and0.81%,respectively.GM only required a small amount of data(at least four data).Therefore,GM could be applied successfully in predicting the co-melting temperature of MSWI fly ash and SSA when no sufficient information is available.It also indicates that both the composition of MSWI fly ash and SSA could be applied on the prediction of co-melting temperature.KeywordsMunicipal solid waste incinerator,sewage sludge ash,co-melting temperatures,grey model,artificial neural networkDate received:5September2009;accepted:3March2010IntroductionAccording to the Republic of China(R.O.C.)EPA (Environmental Protection Administration)statistics,by the year2010,there will be more than1000000tons per year of incinerator residues(including bottom ash,fly ash, and scrubber ash)discharged from municipal solid waste incinerators(MSWI)island wide in Taiwan.As the amount of sewage sludge generated from municipal wastewater treat-ment plants(MWWTPs)is steadily increasing year by year with the expansion of population,treatment and utilization of MSWIfly ash and sewage sludge become more important in Taiwan.In past decades,the more acceptable sewage sludge treatment process was landfilling,but this process faced serious challenges because the available space for land-filling became less and less.Scrubber ash,the largest component(about80%by weight)in MSWIfly ash(a mixture of boiler ash,scrubber ash and cyclone ash),makes it difficult to melt MSWIfly ash alone due to the high pouring point(2570 C)of the scrubber ash component CaO(11–35%by weight).Therefore,it is necessary to modify the alkalinity of the main components of the MSWIfly ash and itsfluxes by mixingfly ash with sludge ash from sewage treatment plants.Under this situa-tion,reuse technologies for MSWIfly ash and sewage sludge treatment,such as the melting process,are proposed to con-quer these problems.The principal advantages of the sludge melting process are that most hazardous materials,such as heavy metals,are tightlyfixed in a solid phase,and the slag1Department of Environmental Engineering and Management, Chaoyang University of Technology,Wufeng,Taichung,Taiwan,R.O.C. 2Department of Environmental Engineering,National Ilan University, Ilan,Ilan,Taiwan,R.O.C.3Institute of Environmental Engineering and Management,National Taipei University of Technology,Taipei,Taiwan,R.O.C.4Department of Chemical and Materials Engineering,National Ilan University,Ilan,Ilan,Taiwan,R.O.C.Corresponding author:Kae-Long Lin,Department of Environmental Engineering,National Ilan University,Ilan,Ilan,26047,Taiwan,R.O.C.Email:kllin@.twWaste Management&Research29(3)284–293!The Author(s)2010Reprints and permissions:/journalsPermissions.navDOI:10.1177/0734242X10367862generated by this process can be used as construction mate-rial(Sakai et al.,1990).However,the alkalinity of MSWIfly ash may be modified by mixing it with sludge ash from sewage treatment plants.This step is necessary to reduce the pouring point of MSWIfly ash during co-melting(Lin, 2006).Glassy slag can be generated by melting waste at tem-peratures exceeding1300 C,after which the molten ash is water-quenched or air-cooled.The volume of the resulting slag can be reduced and the slag stabilized such that heavy metals become immobilized in a glassy Si–O matrix;thus, leaching behaviour is improved.The melting process is oper-ated at high temperature and in a rapid quenched rate, obtaining a product consisting of very irregularly shaped granules of which the main merits are their high durability against chemical erosion and high volume reduction effect. Against this,one of the main disadvantages of the co-melting process is its energy consumption.MSWIfly ash and sewage sludge ash(SSA)composition could affect the co-melting temperatures of slag,particularly the high alkalinity of MSWIfly ash.If the relationship between this composition and the co-melting temperatures could be established,the co-melting temperatures could be predicted and controlled accurately.Thus,energy conservation could be achieved.For model-based predictive control,models should be kept simple and identifiable from measured data. Some soft computation techniques,such as artificial neural network(ANN),in which the reaction mechanisms can be ignored are available presently.Although ANN can predict co-melting temperatures,many data is required for further calculation.In order to gain consistent results from the inves-tigation data and predict co-melting temperatures with few data,the grey system theory(GST)is a suitable method.The GST proposed by Deng(1989)can solve the problem of incomplete data and has been applied in several studies (Pai et al.,2007a,b,2008a,b;Pai,2008).GST focuses on the relational analysis,model construction,and prediction of the indefinite and incomplete information.It requires only a small amount of data and the better prediction results can be obtained.There are several methods in GST including grey model (GM).GM can be used to establish the relationship between many sequences of data and their coefficients can be used to evaluate which sequence of data affects the system significantly.Pai et al.(2007b)used GM to predict the efflu-ent quality from several wastewater treatment plants and obtained accurate results.However,it is difficult to use MSWIfly ash and SSA composition in co-melting tempera-ture modelling.If the relationship between the composition of MSWIfly ash and SSA and co-melting temperatures can be modelled,a better control strategy could be sought.The melting process is operated at high temperature and in a rapid quenched rate,obtaining a product consisting of very irregularly shaped granules of which the main merits are their high durability against chemical erosion and high volume reduction effect but one of the main disadvantages of the co-melting process is its energy consumption.The objectives of this study were:(1)to use GM(0,N)to calcu-late the weight andfind out the composition of MSWIfly ash and SSA which affect co-melting temperatures significantly;(2)to use GM(1,N),GM(1,1),and RGM(1,1)to establish the composition characteristics of MSWIfly ash and SSA for predicting the co-melting temperatures;and(3)to use ANN for comparison purposes to predict the co-melting temperatures in this study.Materials and methodsSewage sludge ash and MSWI flyash preparationThefly ash used in this study was collected from the cyclone of a mass-burning incinerator located in the northern part of Taiwan.The incinerator,capable of processing1350tonnes of local municipal solid waste per day,is equipped with air pollution control devices(APCD)consisting of a cyclone,a semi-dry scrubber system and a fabric bag-housefilter.The incinerator was constructed in1995.The plant includes three Martin stoker units,each with incineration capacity of450 tonnes day–1and three boiler units,each capable of generat-ing39.15tonnes h–1steam at40bar and400 C with super-heaters.In total,200kg offly ash was obtained from the incineration plant.Then,thefly ash was homogenized, oven dried at105 C for24h,and desiccated before testing.A dewatered sludge cake sample was heated in a brick-firing kiln at a temperature of900 C for1h.The properties of the four types of sewage sludge used are outlined in Table1.The MSWIfly ash and the sewage sludge ashesTable1.Properties of sewage sludgeType ofsludge ash Sewer system Wastewatertreatment process Digestion process Conditioning processBL-Ash Combined sewer system Primary treatment–Polymer conditioned sludge JJ-Ash Combined sewer system Primary treatment Anaerobic digestion Polymer conditioned sludge SC-Ash Separated sewer system Secondary treatment Anaerobic digestion Polymer conditioned sludge NH-Ash Separated sewer system Secondary treatment Aerobic digestion Polymer conditioned sludgeand lime stabilityPai et al.285were homogenized,oven dried at105 C for24h,after which the chemical composition was characterized.Preparation of slag from MSWI fly ash and sludge ashes by co-melting treatmentMSWIfly ash was mixed with various amounts of sewage sludge ash.In this study,MSWIfly ash and sewage sludge ashes werefirst ground,then varying composite fractions were well mixed to obtain the test samples.The different proportions used in the melting process are shown in Table2.During the formation of slag,the softening,melting and pouring points were observed and recorded.The molten slag was then water-quenched to produce afine slag,which was further pulverized in a ball mill until the particles could pass through a#200mesh sieve(0.074mm).The resultant pulverized slag had a specific surface area(on Blaine)of approximately300–350m2kg–1,with a specific gravity of 2.7–2.9.The resultant pulverized slag was desiccated before being tested.AnalysesChemical composition and physical analyses of thefly ash, sludge ash and synthetic slags were determined by X-rayflu-orescence(XRF).XRF was performed with an automated RIX2000spectrometer.The samples were prepared for XRF analysis by mixing0.4g of the sample and4g of100 Spectroflux,at a dilution ratio of1:10.Homogenized mix-tures were placed in Pt–Au crucibles,and treated for1h at 1000 C in an electrical furnace.The homogeneous melted sample was recast into glass beads2mm thick and32mm in diameter.The softening,melting and pouring points of the fly ash and sludge ash mixtures were determined by the ASTM D1857method.Grey modelling processIn a situation where information is lacking,using fewer(at least4)system information,one can create a GM to describe the behaviour of the few outputs.By means of an accumu-lated generating operation(AGO),the disorderly and the unsystematic data may become exponentially behaved such that afirst-order differential equation can be used to charac-terize the system behaviour.Solving the differential equation will yield a time response solution for prediction.Through an inverse accumulated generating operation(IAGO),the fore-cast can be transformed back to the sequence of original series.A grey modelling process is described in the following manner(Figure1).Assume that the original series of data with n samples is expressed as:X f0g¼ðxð0Þð1Þ,xð0Þð2Þ,...,xð0ÞðnÞÞ,where the superscription(0)of X(0)represents the original series.Let X(1)be thefirst-order AGO of X(0),whose elements are generated from X(0):Xð1Þ¼ðxð1Þð1Þ,xð1Þð2Þ,...,xð1ÞðnÞÞ, where xð1ÞðkÞ¼P ki¼1xð0ÞðiÞ,for k¼1,2,...,n.Further oper-ation of the AGO can be conducted to reach the r-order AGO series,X(r):X f r g¼ðxðrÞð1Þ,xðrÞð2Þ,...,xðrÞðnÞÞ,where xðrÞðkÞ¼P ki¼1xðrÀ1ÞðiÞ,for k¼1,2,...,n.The IAGO is the inverse operation of AGO.It transforms the AGO-operational series back to the one with a lower order. The operation of IAGO for thefirst-order series is defined as follows:xð0Þð1Þ¼xð1Þð1Þand xð0ÞðkÞ¼xð1ÞðkÞÀxð1ÞðkÀ1Þfor k¼2,3,...,n.After extending this represen-tation to the IAGO of r-order series,we have xðrÀ1ÞðkÞ¼x rðkÞÀx rðkÀ1Þfor k¼2,3,...,n.The tendency of AGO can be approximated by an exponential function.Its dynamic behaviour is like a form of differential equation.The grey model GM(h,N)thus adopts an n-order differential equa-tion tofit the AGO-operational series.The parameters h and N in GM(h,N)denotes the order and the number of vari-ables concerned in the differential equation,respectively.The GM(h,N)can be generally expressed as(Equation(1))X hi¼0a idðiÞxð1Þ1d t¼X Nj¼2b j xð1Þj kðÞð1Þwhere the parameter a is the developing coefficient and b is the grey input.In this study,four different types of GM were adopted,i.e.GM(1,N),GM(1,1)and rolling GM(1,1) (RGM(1,1)).GM(1,N).According to the definition of GM(h,N),GM (1,N)is that the order in the grey differential equation is equal to1and defined as indicated in Equation(2):xð0Þ1ðkÞþazð1Þ1kðÞ¼X Nj¼2b j xð1Þj kðÞ¼b2xð1Þ2ðkÞþb3xð1Þ3ðkÞþÁÁÁþb N xð1ÞNðkÞð2ÞTable2.Proportions of raw materials used for slag preparationSynthetic slagBL3BL4BL5BL6JJ3JJ4JJ5JJ6SC25SC3SC4SC5NH35NH4NH5NH6 Fly ash70%60%50%40%70%60%50%40%75%70%60%50%75%60%50%40%Sludge ash 30%40%50%60%30%40%50%60%25%30%40%50%35%40%50%60%286Waste Management&Research29(3)where zð1Þ1kðÞ¼0:5xð1Þ1ðkÀ1Þþ0:5xð1Þ1ðkÞfor k¼2,3,4,...,n.Expanding Equation(2),we have Equation(3):xð0Þ1ð2Þþazð1Þ12ðÞ¼b2xð1Þ22ðÞþÁÁÁþb N xð1ÞN2ðÞxð0Þ1ð3Þþazð1Þ13ðÞ¼b2xð1Þ23ðÞþÁÁÁþb N xð1ÞN3ðÞ...xð0Þ1ðnÞþazð1Þ1nðÞ¼b2xð1Þ2nðÞþÁÁÁþb N xð1ÞNnðÞð3ÞTransforming Equation(3)into matrix form,we have Equation(4):xð0Þ1ð2Þxð0Þ1ð3Þ...xð0Þ1ðnÞ2 66 66 66 437777775¼Àzð1Þ1ð2Þxð1Þ2ð2ÞÁÁÁxð1ÞNð2ÞÀzð1Þ1ð3Þxð1Þ2ð3ÞÁÁÁxð1ÞNð3Þ......Àzð1Þ1ðnÞxð1Þ2ðnÞÁÁÁxð1ÞNðnÞ2666666437777775ab2...b N26666643777775ð4ÞThen the coefficients can be estimated by solving matrix, h¼ðB T BÞÀ1B T Y,whereh¼ab2...b N2666666437777775Y¼xð0Þ1ð2Þxð0Þ1ð3Þ...xð0Þ1ðnÞ266666664377777775B¼Àzð1Þ1ð2Þxð1Þ2ð2ÞÁÁÁxð1ÞNð2ÞÀzð1Þ1ð3Þxð1Þ2ð3ÞÁÁÁxð1ÞNð3Þ......Àzð1Þ1ðnÞxð1Þ2ðnÞÁÁÁxð1ÞNðnÞ266666664377777775:The h values represent the weight of comparative series to the referential series.Additionally,the GM(1,N)model could be used for prediction and described as (Equation(5)):^xð0Þ1ðkÞ¼X Nj¼2b j xð1ÞjðkÞÀazð1Þ1ðkÞð5ÞWhen adopting GM(1,N),2,3,4,5,6,7and8parameters with higher weights(GM1N2-1,GM1N3-1,GM1N4-1, GM1N5-1,GM1N6-1,GM1N7-1,GM1N8-1)were taken as the comparative series,respectively.Thus N was equal to3,4,5,6,7,8and9,respectively.The GM(1,N)con-structed in this study represented the relationship between MSWIfly ash and SSA composition and melting tempera-tures with different replacement levels.GM(0,N).According to the definition of GM(h,N),GM (0,N)is that the order in grey differential equation is equal to 0and defined as follows(Equation(6)):azð1Þ1kðÞ¼X Nj¼2b j xð1Þj kðÞ¼b2xð1Þ2ðkÞþb3xð1Þ3ðkÞþÁÁÁþb N xð1ÞNðkÞð6ÞExpanding Equation(6),we have Equation(7):azð1Þ12ðÞ¼b2xð1Þ22ðÞþÁÁÁþb N xð1ÞN2ðÞazð1Þ13ðÞ¼b2xð1Þ23ðÞþÁÁÁþb N xð1ÞN3ðÞ...azð1Þ1nðÞ¼b2xð1Þ2nðÞþÁÁÁþb N xð1ÞNnðÞð7ÞFigure1.The structure diagram of GM.Pai et al.287Transforming Equation(7)into a matrix form,we have Equation(8):zð1Þ1ð2Þzð1Þ1ð3Þ...zð1Þ1ðnÞ2 66 66 4377775¼xð1Þ2ð2ÞÁÁÁxð1ÞNð2Þxð1Þ2ð3ÞÁÁÁxð1ÞNð3Þ.........xð1Þ2ðnÞÁÁÁxð1ÞNðnÞ26666643777775b2=ab3=a...b N=a2666437775ð8ÞThen the coefficients can be estimated by solving matrix, ^h¼ð^B T^BÞÀ1^B T^Y,where^h¼b2=ab3=a...b N=a26666643777775^Y¼zð1Þ1ð2Þzð1Þ1ð3Þ...zð1Þ1ðnÞ2666666437777775^B¼xð1Þ2ð2ÞÁÁÁxð1ÞNð2Þxð1Þ2ð3ÞÁÁÁxð1ÞNð3Þ.........xð1Þ2ðnÞÁÁÁxð1ÞNðnÞ2666666437777775:The^h values represent the weight of comparative series to the referential series.GM(1,1).If the numbers of comparative series were reduced further,the model was GM(1,1).All time series values of melting temperature were used to establish GM(1,1). Then the constructed GM(1,1)was used for prediction.RGM(1,1).In GM(1,1),all time series values of melting temperature were used to establish GM(1,1).Whereas in RGM(1,1),traditionally the time series data of melting temperature used to construct the model were the4data before the point which was considered to be predicted. That is,the model had to be constructed every time step and only4data were used for model construction.In both GM(1,1)and RGM(1,1),the compositions of MSWIfly ash and SSA were ignored.ANNThe ANN modelling approach in which the important oper-ation features of human nervous system is simulated attempts to solve problems by using information gained from past experience to new problems.In order to operate analogous to a human brain,many simple computational elements called artificial neurons that are connected by vari-able weights are used in the ANN.With the hierarchical structure of a network of interconnected neurons,an ANN is capable of performing complex computations,although each neuron,alone,can only perform simple work.The multi-layer perceptron structure is commonly used for pre-diction among the many different types of structures.A typ-ical neural network model consists of three independent layers:input,hidden,and output layers(Figure2).Each layer is comprised of several operating neurons.Input neu-rons receive the values of input parameters that are fed to the network and store the scaled input values,while the calculated results in output layer are assigned by the output neurons.The hidden layer performs an interface to fully interconnect input and output layers.The pattern of hidden layer to be applied in the hierarchical network can be either multiple layers or a single layer.Each neuron is connected to every neuron in adjacent layers before being introduced as input to the neuron in the next layer by a connection weight,which deter-mines the strength of the relationship between two connected neurons.Each neuron sums all of the inputs that it receives and the sum is converted to an output value based on aFigure2.The structure diagram of ANN.288Waste Management&Research29(3)predefined activation,or transfer,function.For prediction problems,a supervised learning algorithm is often adopted for training the network to relate input data to output data. In recent years,the back-propagation algorithm has been widely used for teaching multi-layer neural networks. Traditionally,the algorithm uses a gradient search technique (the steepest gradient descent method)to minimize a function equal to the mean square difference between the desired and the actual network outputs.In this study,the ANN consisted of three independent layers:input,hidden,and output layers.To compare with GM,2,3,4,5,6,7and8,parameters with higher weights (ANN2-1,ANN3-1,ANN4-1,ANN5-1,ANN6-1,ANN7-1, ANN8-1)were taken as the input layer variables,respectively. Meanwhile the melting temperature was the single output layer variable.The hidden layer was comprised of10operating neurons.The calculation was carried out using MATLAB.Error analysisIn order to evaluate the prediction accuracy of GM and ANN,the mean absolute percentage error(MAPE)was employed,given by Equation(10):MAPE¼1NX xð0ÞðkÞÀ^xð0ÞðkÞxð0ÞðkÞÂ100%ð10Þwhere xð0ÞðkÞis the investigation value,^xð0ÞðkÞis the predic-tion value.Results and discussionCharacterization of sewage sludgeashes and MSWI fly ashTable3lists the chemical composition of sludge ashes.The major components of the sludge ashes were SiO2(44.6–76.5%),Fe2O3(4.6–8.1%),and Al2O3(10.3–17.2).Other important components were CaO(0.5–6.8%),P2O5(0.8–10.2)and Na2O(0.01–0.92%).According to XRF ana-lysis,the major components in the MSWIfly ash were CaO(38.4%),Na2O(5.9%)and SO3(4.7%).The CaO existed inlarge amounts in MSWIfly ash due to the injection of a limesolution to remove acidic gases.Other important compo-nents were Fe2O3(0.6%),SiO2(2.3%)and K2O(4.4%).Variation of composition of MSWI fly ashand SSA and co-melting temperaturesThe numbers of data investigated were totally48,asshown in Figure3.Among the total numbers of data,thenumbers for training and testing(predicting)were40and8,respectively.Table3.Chemical analyses of raw materialsSample SiO2(%)Al2O3(%)Fe2O3(%)CaO(%)MgO(%)SO3(%)K2O(%)Na2O(%)P2O5(%)Fly ash 2.330.010.5838.43 1.58 4.65 4.35 5.890.41BL-ash55.0117.207.59 3.87 1.64 1.39 2.670.86 1.45JJ-ash50.0116.238.06 4.75 1.68 3.33 2.610.92 1.03SC-ash76.4610.30 4.570.490.800.24 1.910.010.82NH-ash44.5915.57 6.04 6.83 1.980.56 2.950.9210.21 BL,Ba-Li Sewage Treatment Plant;JJ,Chung-Chou Sewage Treatment Plant;SC,Chung-Hsing-Hsin-Tsun Sewage Treatment Plant a; NH,Nei-Hu Sewage Treatment Plant.Figure3.Variation of composition of MSWI fly ash and SSA and melting temperatures.Pai et al.289Weights of operation parametersAccording to Equation(8),the weights(^h)between the melting temperatures and different composition were calculated.The weights were in the following order: MgO(1914.30)>K2O(650.01)>SO3(321.11)>Al2O3 (141.05)>Fe2O3(127.34)>CaO(71.75)>P2O5(55.697) >SiO2(38.125).Based on the results of GM(0,N),the selected input variables in seven types of GM(1,N)and in seven types of ANN are shown in Table4.SimulationFigure4and5depict the prediction results using different GM and ANN,respectively.The1st to40th values were used for model construction,while the41st to48th values were used for evaluation offitness.Table5shows the results of error analysis.As shown in Table4,in the aspect of model construction,MAPEs between the predicted and investigated values of melting temperature were between1.42and14.41% using GM1N2-1to GM1N8-1.The values were2.07and 1.31%when using RGM(1,1)and GM(1,1),respectively. The MAPEs fell in the range of0.07and0.26%using ANN2-1to ANN8-1.In the aspect of model prediction,the MAPEs were between 1.69and13.20%when adopting seven different GM(1,N)models.The MAPE were1.59and1.31%when GM(1,1)and RGM(1,1)were adopted.The MAPEs fell within the range of0.04and0.50%using different types of ANN.When the number of variables involved GM models increased,the MAPE decreased.Contrarily,the MAPE increased when the number of variables involved in ANN models increased.According to the structure of GM,the more variables were adopted,the more the weight of different variables could be calculated for prediction.It resulted in lower MAPE when more variables were adopted.More vari-ables in ANN would result in the possibility of getting trapped in local minimum.Therefore the MAPE increased when more variables were adopted.In GMs,the MAPE of1.31%was found to be the lowest when using RGM(1,1)to predict melting temperature.This value was higher than those of ANN2-1to ANN8-1by1.27, 1.25,1.24,1.18,1.16,1.14%,and0.81%,respectively.Although a goodfitness could be achieved using ANN too,they required a large quantity of data for con-structing model.Contrarily,GM only required a small amount of data(at least4data).Therefore,GM could be applied successfully in predicting melting temperature of MSWIfly ash and SSA when the information was not suffi-cient.It also indicated that the composition could be applied on the prediction of co-melting temperature of MSWIfly ash and SSA.ConclusionsNine types of GM including GM1N2-1,GM1N3-1, GM1N4-1,GM1N5-1,GM1N6-1,GM1N7-1,GM1N8-1, GM(1,1),and RGM(1,1)were used to predict the co-melting temperature of MSWIfly ash and SSA.The ANN was adopted for comparison purposes.The simulation results can be summarized in the following manner..The major components of the sludge ashes were SiO2(44.6–76.5%),Fe2O3(4.6–8.1%),and Al2O3(10.3–17.2).Other important components were CaO(0.5–6.8%),P2O5(0.8–10.2)and Na2O(0.01–0.92%).According to XRFanalysis,the major components in MSWIfly ash were CaO(38.4%),Na2O(5.9%)and SO3(4.7%)..In the aspect of model prediction,the MAPEs were between1.69and13.20%when adopting seven different GM(1,N)models.The MAPE were1.59and1.31%when GM(1,1)and RGM(1,1)were adopted.The MAPEs fell within the range of0.04and0.50%using different types of ANN.Since a correlation between the composition of MSWIfly ash and SSA and co-melting temperatures was constructed,the constructed GM or ANN could be used in the objective function including linear program-ming or other optimization tools for achieving the best co-melting temperature in future studies..In GMs,the MAPE of1.31%was found to be the lowest when using RGM(1,1)to predict melting temperature.This value was higher than those of ANN2-1to ANN8-1 by 1.27, 1.25, 1.24, 1.18, 1.16, 1.14,and0.81%, respectively..GM only required a small amount of data(at least4data).Therefore,GM could be applied successfully in predicting co-melting temperature of MSWIfly ash and SSA whenTable4.Selected input variables in GM and ANNGM ANN Input variablesGM1N2-1ANN2-1MgO,K2OGM1N3-1ANN3-1MgO,K2O,SO3GM1N4-1ANN4-1MgO,K2O,SO3,Al2O3GM1N5-1ANN5-1MgO,K2O,SO3,Al2O3,Fe2O3GM1N6-1ANN6-1MgO,K2O,SO3,Al2O3,Fe2O3,CaOGM1N7-1ANN7-1MgO,K2O,SO3,Al2O3,Fe2O3,CaO,P2O5GM1N8-1ANN8-1MgO,K2O,SO3,Al2O3,Fe2O3,CaO,P2O5,SiO2GM(1,1)All melting temperature data fortrainingRGM(1,1)Previous4melting temperaturebefore predicted point290Waste Management&Research29(3)。