Modelingofheattransfercoefficient inthe furnace of CFB boilers by artificial neural network approach

Modeling of heat transfer coefficient in the furnace of CFB boilers by artificial neural network approachJaroslaw Krzywanski ⇑,Wojciech NowakCzestochowa University of Technology,Institute of Advanced Energy Technologies,Dabrowskiego 73,42-200Czestochowa,Polanda r t i c l e i n f o Article history:Received 14October 2011Accepted 27March 2012Available online 21April 2012Keywords:Heat transfer Neural networks Modeling CFBa b s t r a c tThe present work introduces a way of predicting the local heat transfer coefficient in the combustion chamber of the circulating fluidized bed boiler (CFB)by the artificial neural network (ANN)approach.Neural networks have been successfully applied to calculate the local overall heat transfer coefficient for membrane walls,Superheater I (SH I,Omega Superheater)and Superheater II (SH II,Wing-Walls)in the combustion chamber of the 260MWe CFB boiler.The previously verified numerical model has been used to obtain the overall heat transfer coefficients,necessary for training and testing the ANN.It has been shown,that the neural networks give quick and accurate results as an answer to the input pattern.The local heat transfer coefficients evaluated using the developed ANN model have been in a good agree-ment with numerical and experimental results.Ó2012Elsevier Ltd.All rights reserved.1.IntroductionHeat transfer in the furnace of a CFB boiler is affected by com-plex factors,such as:suspension density,bed temperature,boiler load,gas velocity,geometry of the chamber and flue gas properties [1–4].Therefore detailed measurements in the furnace are needed to characterize the heat transfer processes.Another way to evaluate the heat transfer coefficient is by the use of multiple equations,correlations and models,given in the lit-erature.Some of them are presented in papers [1,5,6].Author quoted the outlook of Molerus [5]who suggested that a reliable prediction of heat transfer between heat exchanger surfaces and fluidized beds can be achieved best by the application of dimen-sional analysis.The correlations given in literature usually differ from one another and are valid only for limited ranges of operating parameters.It sometimes limits their accuracy and generality as well as there are also limited experimental data of the overall heat transfer coefficient for membrane-walls.A wide-range review and comparison of circulating fluidized bed combustor models was provided by Basu [6].The paper pre-sents two approaches to the performance modeling,i.e.furnace ap-proach and system approach.The furnace approach describes the details of what goes on in the furnace while the system approach takes an interest in system integration.Models usually need some additional data,e.g.to adjust param-eters and sometimes are time consuming in order to obtain accu-rate predictions.The algorithms are often complicated and are based on the solution of complex differential equations [7,8].The adjusting of the parameters also could not be determined immedi-ately,especially for different operating conditions.Another estimation method in engineering analysis and predic-tions,is using the artificial neural network as a tool in energy pre-diction and modeling [7].It is the alternative for above described methods of data handling,considering the complexity of numerical and analytical methods and high costs of empirical experiments [9].The presented work deals with an ANN technique to predict the local overall heat transfer coefficient for membrane-walls in the 260MWe CFB boiler.An ANN model is optimized to predict the overall heat transfer coefficient for membrane-walls depending on the boiler operating parameters.The necessary training samples to train the neural network are calculated using earlier developed program,similar to the methods described in [10–14].2.Calculating conditions of the heat transfer coefficient In order to obtain the heat transfer coefficient,some experi-ments have been carried out on the 260MWe (670t/h steam capacity)CFB boiler operating in PGE Turow Power Plant in Poland [15,16].The dimensions of cross-section area of the combustion chamber in its lower part immediately above the grid is equal to 21.2Â5.2m.Then,the cross-section area increases to reach dimensions of 21.2Â9.9m at a height of 6.7m above the grid le-vel.The total height of the combustion chamber is 48m.Two out-let windows,each of dimensions of 7.8Â3.4m,are situated in this way that the axis of cross-section area is located at a level of 38m.0017-9310/$-see front matter Ó2012Elsevier Ltd.All rights reserved./10.1016/j.ijheatmasstransfer.2012.03.066Corresponding author.Tel./fax:+48343250933.E-mail address:jkrzywanski@tlen.pl (J.Krzywanski).The combustion chamber is made of membrane-walls.It is a tight structure with an area of2477m2consisted of tubes with the inner diameter of63.5mm and with88mm pitch for the front and rear walls and65mm for the side walls.The Superheater I is made of7horizontally placed U-tube bun-dles at a distance of1056mm from one another.Each bundle con-sists of two sections:top and bottom.Bottom section is composed of15tubes with a diameter of51mm each,placed one above the other with the distance of63.5mm.The top section consists of32 tubes with a diameter of44.5mm.The distance between the axes of each tube is equal to56mm.The height of thefirst section is 889mm and1736mm of the other.The vertical distance between the axes of the two tube sections is equal to1064mm.The surface of the Omega superheater is equal to770m2.On the basis of the data obtained from the operating the670t/h steam capacity CFB boiler operating in PGE Turow Power Plant a heat transfer model has been created to predict the local overall heat transfer coefficient for membrane-walls,SH I and SH II.The model has been described in details in[17,18]and its validation has been successfully performed using operating data from the boiler.The relative error between value of the overall heat transfer coefficients obtained from experiments and that calculated by the numerical model is about10%.Such error confirms the ability of the model to use it in calculations of the overall heat transfer coefficient.The model has been used here to obtain the necessary training samples to learn the neural network.3.Development of an ANN-based heat transfer algorithm3.1.Neural network modelingArtificial neural networks are the alternative methods to simu-late uncertain,ill-defined,big and complex systems[19].They are useful especially in:optimization,robotics,forecasting,recognition of signal patterns and in system modeling,medicine and power systems,including heating and heat transfer analysis,solar radia-tion,modeling and control of power generation systems,load fore-casting and prediction[7,10,14,19–22].Some of the most important applications are listed in the paper[7].Author describes a wide range offields for modeling and prediction in energy engi-neering system.All the ANN applications are divided into the fol-lowing groups:classification,forecasting,control systems, optimization and decision-making.Author gives some examples, like modeling of the combustion processes in incineration plants, the predictive control of a thermal plant and modeling of the chemical reactions in turbulent combustion simulations[23–25].Other applications of the ANN are shown in papers[12,19].In thefirst paper author presents a procedure of using an artificial neural network for calculating thefluid-to-particle heat transfer coefficient.In the second work artificial neural networks are used as the tools for thermal analysis in engineering systems,especially in heat exchangers.Neural networks operate like a‘‘black box’’and their learning process resembles a human brain operation[8,21].They do not need any detailed information about the studied phenomena,be-cause they learn the relationship between the input and output variables,from examples.They also have ability to ignore redun-dant and excess data,to use incomplete data sets and to concen-trate on more important inputs[7,10].A neural network is formed by a group of interconnected ele-ments called neurons,arranged in three kinds of layers:input, intermediate(so-called hidden)and output layer.They can containNomenclaturef(x)activation energyh local overall heat transfer coefficient value,WmÀ2KÀ1 HIGH the maximum normalized data valueLOW the minimum normalized data valuem the load of the boiler,%n number of samplesN iter number of epochsT temperature,Kv velocity,msÀ1W ACTUAL the actual valueW MAXIMUM the highest value of the parameterW MINIMUM the lowest value of the parameter W NORM the normalized valuez the distance from the gas distributor,m b slope parameterd relative error,%e voidage,–Subscriptsb bedg gasd desired(target)p predicted by a neural networkFig.1.Heating Surfaces in the260MWe CFB boiler.J.Krzywanski,W.Nowak/International Journal of Heat and Mass Transfer55(2012)4246–42534247one or more hidden layers.Connections between neurons are called weights and have real values.The architecture of an artificial neural network,the number of neurons in hidden layers and the activation function of a neurons, depend on the process(task),hence there are for example recur-rent and feed-forward neural networks.It means,that in order to achieve the required accuracy of neural network estimation,suit-able architecture and the proper number of hidden neurons must be assumed.The feed-forward neural network is the ANN type that is widely used for engineering applications[19].Before a neural network becomes a useful modeling tool,it has to be prepared by means of the following principal steps:Step1:setting initial random values of weights and optimizing the ANN.Step2:run the normalization process of input and output parameters.Step3:run the learning(training)procedure.Initial values of weights are set randomly and uniformly distrib-uted between0and1.Because of the fact,that input and output parameters have dif-ferent physical units and range sizes there is a necessity to bring all input and output values to the same numerical range(between0 and1)by the normalization process.It also allows to avoid any computational difficulty[8].The learning stage,also called an epoch is the supervised learn-ing,when the input pattern is repeatedly presented with its corre-sponding output pattern.During training process connection weights are modified using a suitable learning method.The knowl-edge about the relationships between input and output parame-ters,gained by the ANN during learning epoch,is kept in ANN structure and weights adjusted to produce the desired(target)out-put[7,13].To train the network well,sufficient number of input parame-ters must be used,covering the whole range of variables.The most popular learning algorithm,used to train artificial neu-ral networks with one or more hidden layers is Back Propagation (BP)scheme.It is an iterative gradient algorithm for minimizationof the mean square error,between the desired and predicted output[8].The Back Propagation algorithm is considered as a simple,powerful and reliable training method[7,11].During the learning(training)epoch the neural network out-puts are compared with the pattern.The obtained difference isthe measure of the weights modification rate in BP scheme.The most commonly used activation functions in such neuralnetworks are:the logarithmic sigmoid(Eq.(1))and the hyperbolictangent sigmoid function(Eq.(2))[22]:fðxÞ¼1=ð1þe b xÞð1ÞfðxÞ¼ðe xÀeÀxÞ=ðe xþeÀxÞð2ÞThe learning process stops when the criterion of the mean squareerror is fulfilled and the network has good ability to generalizethe obtained knowledge,i.e.to predict accurately of the validationdata set.After the training epoch,neural networks can be used to achieveadequate response i.e.output data via non-iterative calculationswith a low processing time and small memory resources,as ananswer to a new stimuli,not previously presented to the network[12,20].3.2.Application of neural networkThe idea of the neural network use to obtain convective heattransfer coefficient in the circulatingfluidized bed was presentedin the paper[22].The basis of the idea was to create model simple,non-iterative tool to calculate the heat transfer coefficient.As usual the heat-transfer coefficient has been determined dur-ing laborious experiments and the question is:are obtained valuesstill valid when boiler’s operational parameters change?In such asituation it is often necessary to make another experiment.Model-ing using artificial neural network is then much simpler,easier andfaster in such cases.The architecture of the neural network used in the paper isshown in Fig.2.The neural network has been made of four layers:input layer,two hidden layers and output layer.The number of neurons in the input and output layer are thesame as the number of input and output parameters.The inputparameters are:the distance from the gas distributor z,the bedtemperature T b and voidage e b,flue gas velocity v g and the load of the boiler m.Values of input parameters used for training andtesting the ANN are given in Tables1–3.Table1The input parameters used for training and testing the ANN for membrane-walls.Input parameter Range of valuesLoad of the boiler,%40,70,100Distance from the gas distributor,m 6.25–41.7Flue gas velocity,msÀ1 2.11–6.0Average bed voidage,–0.973–0.997Bed temperature,K930–1298Table2The input parameters used for training and testing the ANN for SH I.Input parameter Range of valuesLoad of the boiler,%40,70,100Distance from the gas distributor,m20.25–23.75Flue gas velocity,msÀ1 2.37–5.502Average bed voidage,–0.988–0.992Bed temperature,K1066–1203Table3The input parameters used for training and testing the ANN for SH II.Input parameter Range of valuesLoad of the boiler,%40,70,100Distance from the gas distributor,m30.75–41.75Flue gas velocity,msÀ1 2.11–5.538Average bed voidage,–0.994–0.997Bed temperature,K931–1161 4248J.Krzywanski,W.Nowak/International Journal of Heat and Mass Transfer55(2012)4246–4253The output variable is the local overall heat transfer coefficient value h.The input layer consists offive neurons and the output layer contains one neuron.Normalisation of input and output signals was performed using the formula(Eq.(3))[10]:W NORM¼ðW ACTUALÀW MINIMUMÞ=ðW MAXIMUMÀW MINIMUMÞÃðHIGHÀLOWÞþLOWð3Þwhere:HIGH=0.9,LOW=0.1.During calculation,Lee and Park’s algorithm is used for weighing factors modifications.This method is an instance of Back Propagation scheme where momentum and learning rate change simultaneously during training phase[26].In order to select the optimal configuration,the number of neu-rons in hidden layers and the activation function of a neurons the four error measures have been used:the coefficient of determina-tion R2of the linear regression line between the predicted values from the neural network and the desired output,the mean abso-lute error MAE,the standard deviation of the mean absolute error STD MAE,the mean relative error MRE and the standard deviation of the mean relative error STD MRE[11,12].The numerical data sets consisted of64,29and69input and out-put data pairs,for membrane-walls,SH I and SH II,respectively.Table4Errors of the overall heat transfer coefficient predictions for membrane–walls for different ANN with hyperbolic tangent sigmoid activation function(bold values refers to the optimal ANN configuration).Model Activation function Structure R2MAE MRE STD MAE STD MRE1The hyperbolic tangent sigmoid function5-1-1-10.6804 3.320.02 3.52 4.88 25-1-2-10.6950 3.200.02 3.48 4.77 35-1-3-10.7912 2.810.02 2.71 3.94 45-1-4-10.8119 2.700.02 2.53 3.74 55-1-5-10.7780 2.720.02 2.98 4.07 65-2-1-10.7045 3.570.02 2.96 4.69 75-2-2-10.6721 3.450.02 3.48 4.94 85-2-3-10.7103 3.230.02 3.27 4.65 95-2-4-10.7604 3.110.02 2.78 4.22 105-2-5-10.7257 3.020.02 3.32 4.52 115-3-1-10.7356 3.010.02 3.20 4.44 125-3-2-10.7383 3.040.02 3.15 4.42 135-3-3-10.8263 2.540.02 2.50 3.60 145-3-4-10.8979 2.440.02 1.18 2.75 155-3-5-10.8567 2.220.01 2.36 3.27 165-4-1-10.8282 2.680.02 2.31 3.58 175-4-2-10.6603 3.840.03 3.16 5.03 185-4-3-10.8518 2.420.02 2.22 3.32 195-4-4-10.8724 2.130.01 2.19 3.08 205-4-5-10.8413 3.270.020.81 3.43 215-5-1-10.7969 2.810.02 2.63 3.89 225-5-2-10.7453 3.110.02 2.99 4.36 235-5-3-10.7821 2.880.02 2.75 4.03 245-5-4-10.7819 2.810.02 2.83 4.03 255-5-5-10.8919 2.340.02 1.52 2.83Table5Errors of the overall heat transfer coefficient predictions for membrane–walls for different ANN with logarithmic sigmoid activation function(bold values refers to the optimal ANN configuration).Model Activation function Structure R2MAE MRE STD MAE STD MRE1The logarithmic sigmoid function5-1-1-10.5915 5.130.04 1.68 5.50 25-1-2-10.6992 3.960.02 2.45 4.73 35-1-3-10.6900 4.240.03 2.07 4.80 45-1-4-10.6870 3.620.02 3.11 4.83 55-1-5-10.6865 3.270.02 3.50 4.84 65-2-1-10.6815 4.370.03 1.94 4.86 75-2-2-10.6879 3.460.02 3.29 4.82 85-2-3-10.6249 4.940.04 1.54 5.27 95-2-4-10.7578 3.350.02 2.52 4.24 105-2-5-10.7335 3.040.02 3.20 4.46 115-3-1-10.7770 2.870.02 2.84 4.08 125-3-2-10.7384 3.910.03 1.87 4.41 135-3-3-10.6240 4.330.03 2.91 5.29 145-3-4-10.8160 2.910.02 2.21 3.70 155-3-5-10.7945 2.860.02 2.61 3.91 165-4-1-10.8234 3.240.02 1.47 3.62 175-4-2-10.6069 4.570.03 2.73 5.40 185-4-3-10.6736 3.460.02 3.44 4.93 195-4-4-10.8024 2.890.02 2.45 3.84 205-4-5-10.7349 3.630.03 2.45 4.44 215-5-1-10.7714 3.380.02 2.26 4.12 225-5-2-10.7229 3.130.02 3.23 4.55 235-5-3-10.6488 3.660.02 3.49 5.12 245-5-4-10.6992 3.360.02 3.26 4.73 255-5-5-10.7465 3.280.02 2.77 4.34J.Krzywanski,W.Nowak/International Journal of Heat and Mass Transfer55(2012)4246–42534249Some of them have been utilized for verification of the network and show its ability to correctly predict the output value.For the purpose of testing a network also new,unseen before,data have been used.Because of the fact,that the performance of an ANN depends on its structure,different ANN architectures have been studied.The number of hidden neurons have been varied and changed from1 to5in each hidden layer.Such assumption has been made in order to reduce the risk of memorization instead of generalization the relationships within the data set[27].Two activation functions have also been considered:the loga-rithmic sigmoid and hyperbolic tangent sigmoid function.This have resulted in a total of50networks for membrane-walls and 25networks for SH I and SH II.In order to avoid the problem of over-training the number of learning and testing cycles has been limited to100,000.The four,before mentioned error measures and the coefficient of determination values for different ANN configurations are pre-sented in Tables4–7.The optimal networks have been selected from generated net-works,based on above described errors.3.3.Selecting of the optimal structure3.3.1.Membrane-wallsThe data presented in Table4refer to hyperbolic tangent sig-moid whereas in Table5to logarithmic sigmoid activation functionTable6Errors of the overall heat transfer coefficient predictions for SH I and different ANN with hyperbolic tangent sigmoid activation function(bold values refers to the optimal ANN configuration).Model Activation function Structure R2MAE MRE STD MAE STD MRE1The hyperbolic tangent sigmoid function5-1-1-10.9493 2.650.02 1.10 2.93 25-1-2-10.9710 1.270.01 1.80 2.22 35-1-3-10.9860 1.240.010.87 1.54 45-1-4-10.9492 2.050.01 2.05 2.93 55-1-5-10.99680.480.000.560.74 65-2-1-10.9854 1.160.01 1.04 1.57 75-2-2-10.99540.630.000.600.88 85-2-3-10.99590.700.000.430.83 95-2-4-10.9810 1.210.01 1.30 1.80 105-2-5-10.9892 1.130.010.70 1.35 115-3-1-10.9044 2.860.02 2.77 4.03 125-3-2-10.9570 2.070.01 1.67 2.70 135-3-3-10.99530.690.000.550.89 145-3-4-10.99650.560.000.520.77 155-3-5-10.99380.800.000.61 1.02 165-4-1-10.9771 1.450.01 1.30 1.97 175-4-2-10.99640.550.000.550.78 185-4-3-10.9881 1.180.010.76 1.42 195-4-4-10.99420.840.010.500.99 205-4-5-10.99670.510.000.530.74 215-5-1-10.99230.820.010.77 1.14 225-5-2-10.99490.760.000.500.93 235-5-3-10.99410.750.000.64 1.00 245-5-4-10.99630.560.000.550.80 255-5-5-10.99620.650.000.450.81Table7Errors of the overall heat transfer coefficient predictions for SH II and different ANN with hyperbolic tangent sigmoid activation function(bold values refers to the optimal ANN configuration).Model Activation function Structure R2MAE MRE STD MAE STD MRE1The hyperbolic tangent sigmoid function5-1-1-10.9792 2.510.02 1.44 2.94 25-1-2-10.9923 1.580.010.80 1.79 35-1-3-10.9945 1.230.010.84 1.51 45-1-4-10.9945 1.270.010.78 1.51 55-1-5-10.9952 1.310.010.47 1.42 65-2-1-10.9909 1.650.010.98 1.95 75-2-2-10.9924 1.410.01 1.06 1.79 85-2-3-10.9957 1.030.010.84 1.34 95-2-4-10.99760.790.010.60 1.00 105-2-5-10.99810.750.000.470.90 115-3-1-10.9904 1.820.010.74 2.00 125-3-2-10.9912 1.660.010.89 1.92 135-3-3-10.9892 1.710.01 1.20 2.12 145-3-4-10.9926 1.550.010.76 1.76 155-3-5-10.99650.790.010.90 1.21 165-4-1-10.9900 1.520.01 1.34 2.05 175-4-2-10.99780.880.010.360.97 185-4-3-10.99710.940.010.51 1.09 195-4-4-10.9961 1.150.010.49 1.27 205-4-5-10.9908 1.680.010.95 1.96 215-5-1-10.9925 1.440.010.97 1.76 225-5-2-10.9955 1.180.010.67 1.38 235-5-3-10.99670.960.010.66 1.18 245-5-4-10.99710.910.010.60 1.10 255-5-5-10.9934 1.390.010.87 1.66 4250J.Krzywanski,W.Nowak/International Journal of Heat and Mass Transfer55(2012)4246–4253of the neural network.As it can be seen,ANNs build on tangent sig-moid activation function,give higher coefficient of determination and lower errors.The best ANN architecture is:[5-3-4-1]with hyperbolic tangent sigmoid activation function and[5-4-1-1]with logarithmic sigmoid activation function.Among the two above listed ANN structures,the network with hyperbolic tangent sigmoid activation function is characterized by higher value of coefficient R2(0.8979)and lower errors than it is for logarithmic sigmoid function.Based on observations of the learning process,the neural net-work with the hyperbolic tangent sigmoid activation function need fewer epochs for correct learning of the process than it was in the case of networks with the logarithmicThe training of neural networks withsigmoid activation function proceededmean square error decreases fasterlogarithmic sigmoid activation function.So the[5-3-4-1]ANN with hyperboliction function is the optimal ANNhas been used for further calculations.The[5-3-4-1]type network composes ofi.e.three neurons in thefirst and fourlayer.After learning stage ANNs have beentraining and the new ones.Local heat transfer coefficient values fordicted by the selected[5-3-4-1]neuraltangent sigmoid activation function andmodel are shown as examples in Table8.In the relationship with numericalANN with hyperbolic tangent sigmoidcated in borders of±4%.As it can be seen from the Table8theand h d for some of the data,even for datawork(not used for training,new data)isIt proofs good accuracy of the neuralFig.3the numerical values have beentained by[5-3-4-1]type of ANN.Thisfigurebetween the predicted and desired value.dicts the value of the local overall heatmembrane walls i.e.the ANN model predictscompared to the numerical data.Local heat transfer coefficient values,neural network with logarithmic sigmoidobtained by numerical model are shown in Table9.In Fig.4the numerical values was compared with data obtained by[5-4-4-1]type of ANN with logarithmic sigmoid activation function.As it can be seen in the Table9,the number of epochs N iter is equal to9682whereas for the[5-3-4-1]type ANN with hyperbolic tangent sigmoid activation function the N iter=6630.Data obtained by ANN with logarithmic sigmoid activation function are located in borders of±5%in the relationship to numer-ical results.So the relative errors are higher than it is in the case of ANN with tangent sigmoid activation function.This confirms the poorer ability of the[5-4-4-1]type ANN with logarithmic sigmoid activation function to correctly predict the lo-cal overall-heat transfer coefficient.3.3.2.Superheaters:SH I and SH IIOn the basis of the experience form the previous chapter only hyperbolic tangent sigmoid function have been considered as the activation function.This have resulted in a total of25networks for each examined heating surface.The four error measures and the coefficient of determination values for different ANN architectures are presented in Tables6 and7.Table6refers to SH I and Table7to SH II,respectively.Table8The selected values of the local heat transfer coefficient for membrane-walls, predicted by the[5-3-4-1]type ANN with hyperbolic tangent sigmoid activation function and obtained by numerical method.h d N iter=6630h p dW mÀ2KÀ1W mÀ2KÀ1% Data used for training network150.32146.88 2.29parison of the local overall heat transfer coefficient values desired and predicted for membrane-walls by[5-3-4-1]type ANN with tangent sigmoid activation function.Table9The selected values of the heat transfer coefficient for membrane-walls,predicted by the[5-4-4-1]type ANN with logarithmic sigmoid activation function and obtained by numerical method.h d N iter=9682h p dWmÀ2KÀ1WmÀ2KÀ1%Data used for training network150.32146.32 2.66149.11145.93 2.14138.31140.86 1.85136.77140.07 2.41131.51133.55 1.55 Data not used for training network153.91147.14 4.40152.91146.90 3.93140.30141.600.93139.23141.22 1.43133.11134.62 1.13J.Krzywanski,W.Nowak/International Journal of Heat and Mass Transfer55(2012)4246–425342514252J.Krzywanski,W.Nowak/International Journal of Heat and Mass Transfer55(2012)4246–4253parison of the local overall heat transfer coefficient values desired andpredicted by[5-1-5-1]type ANN for SH I.parison of the local overall heat transfer coefficient values desired andpredicted by[5-2-5-1]type ANN for SH II.Thesefigures show good agreement between the predicted and desired value.The neural networks correctly predict the local heat transfer coefficient for SH I and SH II.The ANN model can be easily used for calculation of overall heat transfer coefficient for membrane-walls and superheaters in the combustion chamber of a CFB boiler.Important feature is the fact, that it is the non-iterative procedure.Theflow chart of ANN appli-cation is shown in Fig.7.4.ConclusionsIn the present study,we have applied the ANN model to accu-rately determine the local overall heat transfer coefficient for the membrane-walls and superheaters SH I and SH II in the CFB boiler furnace.To train the network BP algorithm has been used.The model gives quick and accurate results for any input pattern of the boiler operating parameters(under different conditions).The data obtained using the ANN model are close to that from numer-ical calculations.Maximum relative error has been less than4%for membrane-walls and2%for superheaters.Some of them have been smaller than2%.The ANN model,especially with tangent sigmoid activation function,has been able to predict the local overall heat transfer coefficient accurately.It has been capable to generalize the depen-dence of the local overall heat transfer coefficient for membrane-walls and superheaters on boiler’s operational parameters.ANN could be very helpful tool for simulation the behavior and the opti-mization purposes of the examined systems.References[1]P.Basu,P.K.Nag,Heat transfer to walls of a circulatingfluidized-bed furnace,Chem.Eng.Sci.51(1)(1996)1–26.Review Article No48.[2]C.Breitholtz,B.Leckner,A.P.Baskakov,Wall average heat transfer in CFBboilers,Powder Technol.120(2001)41–48.[3]R.Divilio R.,T.J.Boyd,Practical implication of the effect of solids suspensiondensity on heat transfer in large scale CFB boilers,in:Proc.4th Int.Conf.Circulating Fluidized Beds,New York,AIChE,1994,pp.334–339.[4]W.C.Yang,Handbook of Fluidization and Fluid-Particle Systems,MarcelDekker Inc,2003.[5]O.Molerus,Fluid dynamics and its relevance for basic features of heat transferin circulatingfluidized beds,in:Proc.4th Int.Conf.Circulating Fluidized Beds, New York,AIChE,1994,pp.285–390.[6]P.Basu,Combustion of coal in circulatingfluidized-bed 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