July Pg 21 to 44
TECHNICAL PAPER
Modelling and Optimisation of Specific Fuel Consumption (with Oxygen Enriched Preheated Air) in Rotary Furnace Using Feed Forward Modelling Method of ANN R, K. Jain*, B. D a** and A yub Khan** D.. Gupt Gupta** Ayub *Director, B.S.A. College of Engg. & Tech. Mathura, **Director, A.P., Anand Engg. College Agra
This paper deals with modelling and optimisation of specific fuel consumption in a LDO-fired rotary furnace using feed forward modelling method of artificial neural network (ANN). The authors conducted experimental investigations on fuel consumption in a rotary furnace in an industry. It was observed that approx. 8% oxygen enrichment of the air preheated upto 4760C simultaneously with reduction of air volume to 60% of its theoretical requirement lowered the specific fuel consumption to 0.208 lit/kg. The compact heat exchanger with 533 fins was used for preheating the air. Accordingly, the emission levels were also considerably reduced. The feed forward modelling method of artificial neural network contained in MATLAB software was used for modelling and optimisation of specific fuel consumption. The percentage variation between actual experimental data and modelled result is 1.28%, which is fairly acceptable.
Keyw or ds : Rotary furnace, Excess air percentage, Preheat air eywor ords temperature, oxygen enrichment, feed forward modelling, artificial neural networks, energy consumption.
Literature Review W.W. Levi[1] was the first person to develop a mathematical model between carbon content in the charge and that of tapped metal. Pehlke[2] developed the first thermo-chemical model for predicting cupola performance under various operating conditions. Landefeld and Katz[3] developed a kinetic model for carbon pickup in cupola based on carbon activity. Sahajwala[4] et al. have estimated the extent of carburisation and re-carburisation of the solid charge in stack of cupola and found it to be negligible. Sahajwala and Pehlke[5] pointed out accurate control of carbon content depend upon identifying the phenomena which controls it. Stanik et al. [6] has
developed similar mathematical models. Karunakar and Datta[7] has successfully applied artificial neural networks in the control of cupola furnace. Bishop Christopher M.[8] explained the working and importance of neural networks in modelling and optimisation. Haykins Symon [9] successfully applied the single layer and multilayer network architecture for neural networks in modelling and optimisation.
INTRODUCTION-Network Architectures[8,9]–Multilayer Feed Forward Neural Networks This class of feed forward neural network contains one or more hidden layers whose computation nodes are called hidden neurons or hidden units. The function of hidden neurons is to intervene between the external input and network output in useful manner. By adding one or more hidden layers, the network is enabled to extract higher order statistics. The source nodes in input layer of the network supply respective elements of the activation pattern which constitutes the input signals applied to the neurons in the second layer (first hidden layer). The output signals of the second layer are used as input to the third layer and so on for rest of the network to the activation pattern supplied by the source nodes in the input (first) layer. The architectural graph in Fig. 1 illustrates layout of multilayer feed forward network for single hidden layer. The feed forward network with m source nodes, h1 neurons in first hidden layer, h 2 neurons in second hidden layer and q neurons in the output layer is referred to as m-h 1 -h 2 -q network. The 27
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TECHNICAL PAPER Feed Forward with Multi-Layer Neurons
Input Layer
Hidden Layer
Output Layer
Fig. 1 : Multilayer Feed Forward Network for Single Hidden Layer. multilayer feed forward network is an important class of neural network which consists of set of source nodes that constitutes the input layer, one or more hidden layer of computation nodes, and an output layer of computation nodes. The input signal propagates through the network on a forward direction on a layer by layer basis. These are referred as multilayer perceptions.
conducted on a 200 kg rotary furnace. A feed forward modelling neural network was constructed to model the rotary furnace data. The network used seven inputs, two hidden layers of seven neurons (nodes) in addition to one node output layer as shown in Fig. 4. The network as mentioned above yielded comparatively better results. The network could predict output parameter within about 5% error. All input and output data are scaled so that they are confined to subinterval of 0-1. In this case, each input or output parameter P is normalised as Pn before being applied to the neural network. The results of tests are shown in following graphs. The conclusion from these modelling experiments is therefore that the tested network appears to constitute a workable model for modelling of rotary furnace parameters. The discrete structure is shown in Fig. 3. Artificial Neural Network 1. Preheat Air temp.
3. Time/Heat
The rotary furnace has proved to be an eco-friendly and energyefficient furnace for ferrous foundries. The energy consumption measured in terms of specific fuel consumption, has reduced significantly. The rotary furnace is a melting unit. The input parameters are:
4. Fuel/Heat
Charge-[fixed 200kg], Fuel (LDO) Flame Temperature Time/Heat Preheated Air Volume Preheated Air Temp Oxygen Consumption
z z z z z z
5. Melting Rate 6. Oxy Consumption 7. Air Consumption Input Layer
First Hidden Layer
Second Hidden Layer
Output Layer
F e e d FFor or war d Netw ork Modelling ward Network
Fig. 3 : Discrete Structure. Procedure Adopted - The following procedure is adopted :
These parameters are to be controlled during melting for minimum specific fuel consumption. ANN modelling of rotary furnace parameters is shown in Fig. 2. INPUT S INPUTS
z
A.N.N. Modelling of Rotary Furnace Parameters
MOLTEN METAL
Fig. 2 : A.N.N. Modelling of Rotary Furnace Parameters.
Objective - (1) Optimal Specific Fuel Consumption (lit/kg) The rotary furnace data is used to train and test. Feed forward neural networks have been extracted from actual experiments
Selection of Training and Testing Data This is one of the most important and crucial parts of ANN model development. If the training data is not appropriate, sufficient and accurate, the ANN model output will not be good. For rotar y furnace modelling using ANN, the experimental data has been collected and 75% of it is used for training and rest 25% is used for testing. The data used for modelling are based on the experimental investigations carried out on a rotary furnace; by approx. 8% oxygen enrichment of 60% theoretically required preheated air. The experimental set of observations are shown in Table-1.
OUTPUT
1. Charge- [fixed 200kg] _______ 2. Fuel (LDO) _______________ 3. Flame Temperature ________ 4. Time / Heat ______________ 5. Preheated Air Volume ______ 6. Preheated Air Temperature __ 7. Oxygen C Consumption ______
Specific Fuel Consumption
2. Flame temp
Modelling and Optimisation of Specific Fuel Consumption in Rotary Furnace
z
Inputs-7 No. of Neurons-7 Output-1
z
Selection of Data for Training and Development of Model Out of 10 sets of observations, seven sets have been selected for training and development of model. The input data selected for training and development of model is shown in Table- 2.
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TECHNICAL PAPER Tabl e-1 : Eff ect of 7.7-8.4% Oxy gen Enrichment of 61.1-64.9% of Theor eticall equir ehe o able-1 Effect Oxygen Theoreticall eticallyy R Requir equiree d Air Pr Prehe eheaa t ed upt upto sing Comp act He a t Ex changer , R ot a ting F urnac e a t Optimal S p e e d of 1.0 rpm, on Flame T emp er a tur e, 476 0C, U Using Compact Hea Exchanger changer, Rot ota Furnac urnace at Sp Temp emper erature, Time, FFuel, uel, Mel ting Ra pecific FFuel uel Consumption Melting Ratt e and SSp Heat No.
R p m Preheated Melting Rate Flame Time / Fuel / Air TTemp emp emp.. ( 0 C) Temp emp.. ( 0 C ) H e a t ( m i n . ) He Heaa t (litr (litree s ) k g / h r
Specific Fuel Oxy gen Cons ./ Air Cons ./ Oxygen Cons./ Cons./ g.) Heat (m 3 ) Heat (m 3 ) Cons.. (lit/k (lit/kg.) Cons
1
1
424.0
1745.0
32.00
48.0
375.0
0.240
49.3
319.0
2
1
430.0
1752.0
32.00
47.0
375.0
0.235
49.0
319.0
3
1
437.0
1755.0
32.00
46.5
375.0
0.232
48.0
317.0
4
1
448.0
1762.0
31.50
45.8
380.9
0.229
46.8
313.0
5
1
465.0
1770.0
31.00
45.0
387.0
0.225
46.0
310.0
6
1
470.0
1772.0
30.50
44.6
393.4
0.223
45.0
309.0
7
1
472.0
1773.0
30.50
43.8
393.4
0.219
45.0
302.0
8
1
474.0
1776.0
30.40
42.9
394.7
0.214
43.0
297.0
9
1
475.0
1778.0
30.10
42.0
398.6
0.210
41.5
295.0
10
1
476.0
1778.0
30.10
41.6
398.6
0.208
40.0
294.0
Table-2 : Input Data Selected for Training and Development of Model Heat No.
Preheated Air F l a m e Temp emp.. ( 0 C) emp.. ( 0 C) Temp
Time /Heat (minut (minutee s)
Fuel/Heat ( l i t rree s )
Melting Rate (kg/hr)
Oxy gen Cons ./ Air Cons/ Oxygen Cons./ Heat (m 3 ) Heat (m 3)
1
424.0
1745.0
32.00
48.0
375.0
49.3
319.0
2
437.0
1755.0
32.00
46.5
375.0
48.0
317.0
3
448.0
1762.0
31.50
45.8
380.9
46.8
313.0
4
465.0
1770.0
31.00
45.0
387.0
46.0
310.0
5
470.0
1772.0
30.50
44.6
393.4
45.0
309.0
6
474.0
1776.0
30.40
42.9
394.7
43.0
297.0
7
476.0
1778.0
30.10
41.6
398.6
40.0
294.0
The output (specific fuel consumption) corresponding to these inputs as per experimental data is given in Table-3.
Table-3 : Output (Specific Fuel Consumption) Corresponding to Inputs of Model
z
Heat No.
S p ecific FFuel uel Consumption (lit/k g) (lit/kg)
1
0.240
2
0.232
3
0.229
4
0.225
5
0.223
6
0.214
7
0.208
Table-4 : Maximum Limits of Inputs for Normalisation SN
Input Inputss
Maximum limit
1
Preheat air temp
500 0 C
2
Flame temp
1780 0 C
3
Time required/heat
33 minutes
4
Fuel required
50 litres
5
Melting rate
400 kg/hr
6
Oxygen consumption
50 m3
7
Preheated air consumption
320 m3
Similarly maximum limit of output is shown in Table-5. Table-5: Maximum Limits of Output for Normalisation
Limits for Normalisation for Inputs Maximum limits of inputs for normalisation are shown in Table-4.
SN
Out put Output
Maximum limit
1
Specific fuel consumption
0.285 litre/kg 29
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TECHNICAL PAPER Normalised Values
z
The normalised values of input data selected for training and development of model as feed to ANN programme of MATLAB are shown in Table-6.
Table-6 : Normalised Values of Input Data of Model 2 Heat No.
Preheated Flame 0 Air TTemp emp emp.. ( C) Temp emp.. ( 0 C)
Time/ Heat (min.)
Fuel / He Heaa t (litr (litree s)
Melting Rate (kg/hr)
Oxygen/ Heat (m 3 )
Air/ Heat (m 3 )
1
0.848
0.9803
0.9696
0.960
0.9375
0.986
0.9968
2
0.874
0.9859
0.9696
0.930
0.9375
0.960
0.9906
3
0.896
0.9898
0.9545
0.916
0.9522
0.936
0.9781
4
0.930
0.9943
0.9393
0.900
0.9675
0.920
0.9687
5
0.940
0.9955
0.9242
0.892
0.9835
0.900
0.9656
6
0.948
0.9977
0.9212
0.858
0.9867
0.860
0.9281
7
0.952
0.9988
0.9121
0.832
0.9965
0.800
0.9187
The normalised values of output (specific fuel consumption) corresponding to inputs as per experimental data are given in Table-7.
Table-7 : Normalised Values of Output of Model 2 Heat No.
S p ecific FFuel uel Consumption lit/k g lit/kg
1
0.8420
2
0.8140
3
0.8035
4
0.7894
5
0.7824
6
0.7508
7
0.7298
Training and Development of Model – MATLAB Programme The ANN (Artificial Neural Network) programme contained in MATLAB is run as shown below—
%p12=[1745 1752 1755 1762 1770 1772 1773 1776 1778 1778]; %p13=[32 32 32 31.5 31 30.5 30.5 30.4 30.1 30.1]; %p14=[48 47 46.5 45.8 45 44.6 43.8 42.9 42 41.6]; %p15=[375 375 375 380.9 387 393.4 393.4 394.7 398.6 398.6]; %p16=[49.3 49 48 46.8 46 45 45 43 41.5 40]; %p17=[319 319 317 313 310 309 302 297 295 294]; %op=[0.2400 0.2600 0.2320 0.2290 0.2250 0.2230 0.2186 0.2140 0.2150 0.2080]; plot (p17,op) xlabel(‘Air/Heat........’); ylabel(‘Specific Fuel.....’);
Effect of Individual Input Parameter on Output (Specific Fuel Consumption) The effect of individual input parameter on output (specific fuel consumption) on basis of training and development of model is shown in following figures z
The Effect of Preheated Air on Specific Fuel Consumption – It is shown in Fig. 4.
clc; clear all; close all; %ip1=[424 437 448 465 470 474 476]; %ip2=[1745 1755 1762 1770 1772 1776 1778]; %ip3=[32 32 31.5 31 30.5 30.4 30.1]; %ip4=[48 46.5 45.8 45 44.6 42.9 41.6]; %ip5=[375 375 380.9 387 393.4 394.7 398.6]; %ip6=[49.3 48 46.8 46 45 43 40]; %ip7=[319 317 313 310 309 297 294]; %op= [0.240 0.232 0.229 0.225 0.223 0.214 0.208]; %p11=[424 430 437 448 465 470 472 474 475 476];
Fig. 4 : Effect of Preheated Air Temperature on Specific Fuel Consumption
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TECHNICAL PAPER z
The Effect of Flame Temperature on Specific Fuel Consumption- It is shown in Fig. 5.
z
Fig. 8 : Effect of Melting Rate on Specific Fuel Consumption.
Fig. 5- Effect of Flame Temperature on Specific Fuel Consumption. z
The Effect of Time/Heat on Specific Fuel Consumption- It is shown in Fig. 6.
z
The Effect of Fuel/Heat on Specific Fuel Consumption – It is shown in Fig. 7.
Fig. 7 : Effect of Fuel/Heat on Specific Fuel Consumption
The Effect of Oxygen/Heat on Specific Fuel Consumption - It is shown in Fig. 9.
Fig. 9 : Effect of Oxygen/Heat on Specific Fuel Consumption (Model 2)
Fig. 6. : Effect of Time/Heat on Specific Fuel Consumption. z
The Effect of Melting Rate on Specific Fuel Consumption- It is shown in Fig. 8.
z
The Effect of Air/Heat on Specific Fuel Consumption – It is shown in Fig. 10.
Fig. 10 : Effect of Air/Heat on Specific Fuel Consumption (Model 2). 31
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TECHNICAL PAPER The output parameters (specific fuel consumption) during training of model are given in Table-8.
Table-8 : Output Parameters (Specific Fuel Consumption) After Training of Model 2. Heat No.
Modell p ecific FFuel uel Modellee d SSp Consumption (lit/kg of Model Model)
1
0.240
2
0.232
3
0.229
4
0.225
5
0.223
6
0.214
7
0.208
Test R un of Model -The Run model so trained and developed is being tested for its validity. The model is tested for all ten sets of observations as per Table-1.
Fig. 12 : Effect of Flame Temperature on Specific Fuel Consumption as per Test Run of Model 2. z
The Effect of Time/Heat on Specific Fuel consumption - It is shown in Fig. 13.
The Effect of Individual Input Parameter on Output (Specific Fuel Consumption) On basis of test running of model, the effect of individual input parameters on output (specific fuel consumption) is shown in following figures
z
The Effect of Preheated Air on Specific Fuel Consumption- It is shown in Fig.11.
z
Fig. 13 : Effect of Time/Heat on Specific Fuel Consumption as per Test Run of Model 2. z
The Effect of Fuel/Heat on Specific Fuel Consumption - It is shown in Fig. 14.
Fig. 11 : Effect of Preheated Air Temperature on Specific Fuel Consumption as per Test Run of Model z
The Effect of Flame Temperature on Specific Fuel consumption- It is shown in Fig. 12.
Fig. 14 : Effect of Fuel/Heat on Specific Fuel Consumption as per Test Run of Model.
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TECHNICAL PAPER z
The Effect of Melting Rate on Specific Fuel Consumption- It is shown in Fig. 15.
The output parameters (specific fuel consumption) of model 2 after test running are given in Table-9.
Table-9 : Output Parameters (Specific Fuel Consumption) of Model as per Test Running Heat No.
Fig. 15 : Effect of Melting Rate on Specific Fuel Consumption as per Test Run of Model. z
The Effect of Oxygen/Heat on Specific Fuel Consumption- It is shown in Fig. 16.
1 2 3 4 5 6 7 8 9 10
Modell p ecific FFuel uel Consumption Modellee d SSp Te st R g.) Run (lit/kg.) un of Model (lit/k 0.2400 0.2600 0.2320 0.2290 0.2250 0.2230 0.2186 0.2140 0.2150 0.2080
Comparison of Outputs The outputs (modelled specific fuel consumption) of above test run of model and the comparison with actual specific fuel consumption is shown in Table-10.
Results The error between actual and modelled specific fuel consumption varies from +0.18% to +10.6%. The average variation is 1.28%. It lies within the acceptable limits of ±10%.
Presentation of Error
Fig. 16 : Effect of Oxygen/Heat on Specific Fuel Consumption as per Test Run of Model. z
The Effect of Air/Heat on Specific Fuel Consumption- It is shown in Fig. 17.
Fig. 17 : Effect of Air/Heat on Specific Fuel Consumption as per Test Run of Model.
The error is presented graphically in Fig. 18 using MATLABclc; clear all; close all; x=[0 0.025 0 0 0 0 -0.0004 0 0.005 0]; y=erf(x) plot(y)
Fig. 18 : Error Graph of Model. 33
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TECHNICAL PAPER Table-10 : Comparison of Modelled and Experimental Specific Fuel Consumption of Model H e a t Preheated F l a m e No. Air Te m p . Temp emp.. ( 0 C) ( 0 C )
Time / Fuel / M e l t i n g Heat Rate Heat ( M i n u t e s ) ( l i t rree s ) ( k g / h r )
Oxygen A i r Modelled Cons/ S p ecific Cons/ H e a t ( m 3) H e a t ( m 3) F u e l (lit/kg)
Actual Absolute P e r c e n S p ecific E r r o r ta g e Fuel Error % (lit/kg.)
1
424.0
1745.0
32.00
48.0
375.0
49.3
319.0
0.2400
0.240
0.000
0.00
2
430.0
1752.0
32.00
47.0
375.0
49.0
319.0
0.2600
0.235
0.025
10.6
3
437.0
1755.0
32.00
46.5
375.0
48.0
317.0
0.2320
0.232
0.000
0.000
4
448.0
1762.0
31.50
45.8
380.9
46.8
313.0
0.2290
0.229
0.000
0.000
5
465.0
1770.0
31.00
45.0
387.0
46.0
310.0
0.2250
0.225
0.000
0.000
6
470.0
1772.0
30.50
44.6
393.4
45.0
309.0
0.2230
0.223
0.000
0.000
7
472.0
1773.0
30.50
43.8
393.4
45.0
302.0
0.2186
0.219
0.004
-0.18
8
474.0
1776.0
30.40
42.9
394.7
43.0
297.0
0.2140
0.214
0.000
0.000
9
475.0
1778.0
30.10
42.0
398.6
41.5
295.0
0.2150
0.210
0.005
2.38
10
476.0
1778.0
30.10
41.6
398.6
40.0
294.0
0.2080
0.208
0.000
0.000
Conclusions The average percentage error of model is 1.28%. The variations of both of these models are much lower than acceptable limits of ±10%. Hence, models are acceptable and further can be used for simulation.
Cupola Reactions –Behavior of Carbon, Silicon and Manganese, Transactions of AFS 1991, Vol.99, pp. 269-276. 5.
V. Sahajiwala and R.D. Pehlke, Experimental Investigations and Mathematical Modeling of Carbon Transport in a Cupola, Transactions of AFS 1992, Vol. 100, pp. 343-352.
6.
V. Stanek, S. Katz, C. F. Landefeld and M. E. Bauer, The AFS Cupola Process Model- A Computer Tool for Foundries, Modern Casting, June 1999, pp. 41-43.
7.
D.B. Karunakar, and G.L. Datta, Modeling of Cupola Furnace Parameters Using Artificial Neural Networks, Indian Foundry Journal, Vol. 48, No. 5, May 2002, pp. 29-39.
8.
Christopher M. Bishop, Neural Networks for Pattern Recognition, Oxford University Press, Sixth Indian Edition pp. 116-119.
9.
Symon Haykins, Neural Networks, Pearson Prentice Hall, pp. 139197.
References 1.
W.W. Levis, Variables Affecting Carbon Control in Cupola, Transactions of AFS 1947, Vol. 55, pp. 626-632.
2.
R.D. Pehlke, Thermo-Chemical Model of Computer Prediction of Cupola Performance, Transactions of AFS 1963, Vol. 71, pp.580-587.
3.
C. F. Landefeld and S. Katz, A Dual Stream Model of Carbon Pickup based on Carbon Activity, Cast Metals ,1976, Vol. 3, pp.163-17.
4.
V. Sahajiwala, R.D. Pehlke, C. F. Lardefeld and S. Katz, Modeling Key
34 Vol 57
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Modelling and Optimisation of Specific Fuel Consumption (with Oxygen Enriched Preheated Air) in Rotary Furnace Using Feed Forward Modelling Method of ANN R, K. Jain*, B. D a** and A yub Khan** D.. Gupt Gupta** Ayub *Director, B.S.A. College of Engg. & Tech. Mathura, **Director, A.P., Anand Engg. College Agra
This paper deals with modelling and optimisation of specific fuel consumption in a LDO-fired rotary furnace using feed forward modelling method of artificial neural network (ANN). The authors conducted experimental investigations on fuel consumption in a rotary furnace in an industry. It was observed that approx. 8% oxygen enrichment of the air preheated upto 4760C simultaneously with reduction of air volume to 60% of its theoretical requirement lowered the specific fuel consumption to 0.208 lit/kg. The compact heat exchanger with 533 fins was used for preheating the air. Accordingly, the emission levels were also considerably reduced. The feed forward modelling method of artificial neural network contained in MATLAB software was used for modelling and optimisation of specific fuel consumption. The percentage variation between actual experimental data and modelled result is 1.28%, which is fairly acceptable.
Keyw or ds : Rotary furnace, Excess air percentage, Preheat air eywor ords temperature, oxygen enrichment, feed forward modelling, artificial neural networks, energy consumption.
Literature Review W.W. Levi[1] was the first person to develop a mathematical model between carbon content in the charge and that of tapped metal. Pehlke[2] developed the first thermo-chemical model for predicting cupola performance under various operating conditions. Landefeld and Katz[3] developed a kinetic model for carbon pickup in cupola based on carbon activity. Sahajwala[4] et al. have estimated the extent of carburisation and re-carburisation of the solid charge in stack of cupola and found it to be negligible. Sahajwala and Pehlke[5] pointed out accurate control of carbon content depend upon identifying the phenomena which controls it. Stanik et al. [6] has
developed similar mathematical models. Karunakar and Datta[7] has successfully applied artificial neural networks in the control of cupola furnace. Bishop Christopher M.[8] explained the working and importance of neural networks in modelling and optimisation. Haykins Symon [9] successfully applied the single layer and multilayer network architecture for neural networks in modelling and optimisation.
INTRODUCTION-Network Architectures[8,9]–Multilayer Feed Forward Neural Networks This class of feed forward neural network contains one or more hidden layers whose computation nodes are called hidden neurons or hidden units. The function of hidden neurons is to intervene between the external input and network output in useful manner. By adding one or more hidden layers, the network is enabled to extract higher order statistics. The source nodes in input layer of the network supply respective elements of the activation pattern which constitutes the input signals applied to the neurons in the second layer (first hidden layer). The output signals of the second layer are used as input to the third layer and so on for rest of the network to the activation pattern supplied by the source nodes in the input (first) layer. The architectural graph in Fig. 1 illustrates layout of multilayer feed forward network for single hidden layer. The feed forward network with m source nodes, h1 neurons in first hidden layer, h 2 neurons in second hidden layer and q neurons in the output layer is referred to as m-h 1 -h 2 -q network. The 27
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TECHNICAL PAPER Feed Forward with Multi-Layer Neurons
Input Layer
Hidden Layer
Output Layer
Fig. 1 : Multilayer Feed Forward Network for Single Hidden Layer. multilayer feed forward network is an important class of neural network which consists of set of source nodes that constitutes the input layer, one or more hidden layer of computation nodes, and an output layer of computation nodes. The input signal propagates through the network on a forward direction on a layer by layer basis. These are referred as multilayer perceptions.
conducted on a 200 kg rotary furnace. A feed forward modelling neural network was constructed to model the rotary furnace data. The network used seven inputs, two hidden layers of seven neurons (nodes) in addition to one node output layer as shown in Fig. 4. The network as mentioned above yielded comparatively better results. The network could predict output parameter within about 5% error. All input and output data are scaled so that they are confined to subinterval of 0-1. In this case, each input or output parameter P is normalised as Pn before being applied to the neural network. The results of tests are shown in following graphs. The conclusion from these modelling experiments is therefore that the tested network appears to constitute a workable model for modelling of rotary furnace parameters. The discrete structure is shown in Fig. 3. Artificial Neural Network 1. Preheat Air temp.
3. Time/Heat
The rotary furnace has proved to be an eco-friendly and energyefficient furnace for ferrous foundries. The energy consumption measured in terms of specific fuel consumption, has reduced significantly. The rotary furnace is a melting unit. The input parameters are:
4. Fuel/Heat
Charge-[fixed 200kg], Fuel (LDO) Flame Temperature Time/Heat Preheated Air Volume Preheated Air Temp Oxygen Consumption
z z z z z z
5. Melting Rate 6. Oxy Consumption 7. Air Consumption Input Layer
First Hidden Layer
Second Hidden Layer
Output Layer
F e e d FFor or war d Netw ork Modelling ward Network
Fig. 3 : Discrete Structure. Procedure Adopted - The following procedure is adopted :
These parameters are to be controlled during melting for minimum specific fuel consumption. ANN modelling of rotary furnace parameters is shown in Fig. 2. INPUT S INPUTS
z
A.N.N. Modelling of Rotary Furnace Parameters
MOLTEN METAL
Fig. 2 : A.N.N. Modelling of Rotary Furnace Parameters.
Objective - (1) Optimal Specific Fuel Consumption (lit/kg) The rotary furnace data is used to train and test. Feed forward neural networks have been extracted from actual experiments
Selection of Training and Testing Data This is one of the most important and crucial parts of ANN model development. If the training data is not appropriate, sufficient and accurate, the ANN model output will not be good. For rotar y furnace modelling using ANN, the experimental data has been collected and 75% of it is used for training and rest 25% is used for testing. The data used for modelling are based on the experimental investigations carried out on a rotary furnace; by approx. 8% oxygen enrichment of 60% theoretically required preheated air. The experimental set of observations are shown in Table-1.
OUTPUT
1. Charge- [fixed 200kg] _______ 2. Fuel (LDO) _______________ 3. Flame Temperature ________ 4. Time / Heat ______________ 5. Preheated Air Volume ______ 6. Preheated Air Temperature __ 7. Oxygen C Consumption ______
Specific Fuel Consumption
2. Flame temp
Modelling and Optimisation of Specific Fuel Consumption in Rotary Furnace
z
Inputs-7 No. of Neurons-7 Output-1
z
Selection of Data for Training and Development of Model Out of 10 sets of observations, seven sets have been selected for training and development of model. The input data selected for training and development of model is shown in Table- 2.
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TECHNICAL PAPER Tabl e-1 : Eff ect of 7.7-8.4% Oxy gen Enrichment of 61.1-64.9% of Theor eticall equir ehe o able-1 Effect Oxygen Theoreticall eticallyy R Requir equiree d Air Pr Prehe eheaa t ed upt upto sing Comp act He a t Ex changer , R ot a ting F urnac e a t Optimal S p e e d of 1.0 rpm, on Flame T emp er a tur e, 476 0C, U Using Compact Hea Exchanger changer, Rot ota Furnac urnace at Sp Temp emper erature, Time, FFuel, uel, Mel ting Ra pecific FFuel uel Consumption Melting Ratt e and SSp Heat No.
R p m Preheated Melting Rate Flame Time / Fuel / Air TTemp emp emp.. ( 0 C) Temp emp.. ( 0 C ) H e a t ( m i n . ) He Heaa t (litr (litree s ) k g / h r
Specific Fuel Oxy gen Cons ./ Air Cons ./ Oxygen Cons./ Cons./ g.) Heat (m 3 ) Heat (m 3 ) Cons.. (lit/k (lit/kg.) Cons
1
1
424.0
1745.0
32.00
48.0
375.0
0.240
49.3
319.0
2
1
430.0
1752.0
32.00
47.0
375.0
0.235
49.0
319.0
3
1
437.0
1755.0
32.00
46.5
375.0
0.232
48.0
317.0
4
1
448.0
1762.0
31.50
45.8
380.9
0.229
46.8
313.0
5
1
465.0
1770.0
31.00
45.0
387.0
0.225
46.0
310.0
6
1
470.0
1772.0
30.50
44.6
393.4
0.223
45.0
309.0
7
1
472.0
1773.0
30.50
43.8
393.4
0.219
45.0
302.0
8
1
474.0
1776.0
30.40
42.9
394.7
0.214
43.0
297.0
9
1
475.0
1778.0
30.10
42.0
398.6
0.210
41.5
295.0
10
1
476.0
1778.0
30.10
41.6
398.6
0.208
40.0
294.0
Table-2 : Input Data Selected for Training and Development of Model Heat No.
Preheated Air F l a m e Temp emp.. ( 0 C) emp.. ( 0 C) Temp
Time /Heat (minut (minutee s)
Fuel/Heat ( l i t rree s )
Melting Rate (kg/hr)
Oxy gen Cons ./ Air Cons/ Oxygen Cons./ Heat (m 3 ) Heat (m 3)
1
424.0
1745.0
32.00
48.0
375.0
49.3
319.0
2
437.0
1755.0
32.00
46.5
375.0
48.0
317.0
3
448.0
1762.0
31.50
45.8
380.9
46.8
313.0
4
465.0
1770.0
31.00
45.0
387.0
46.0
310.0
5
470.0
1772.0
30.50
44.6
393.4
45.0
309.0
6
474.0
1776.0
30.40
42.9
394.7
43.0
297.0
7
476.0
1778.0
30.10
41.6
398.6
40.0
294.0
The output (specific fuel consumption) corresponding to these inputs as per experimental data is given in Table-3.
Table-3 : Output (Specific Fuel Consumption) Corresponding to Inputs of Model
z
Heat No.
S p ecific FFuel uel Consumption (lit/k g) (lit/kg)
1
0.240
2
0.232
3
0.229
4
0.225
5
0.223
6
0.214
7
0.208
Table-4 : Maximum Limits of Inputs for Normalisation SN
Input Inputss
Maximum limit
1
Preheat air temp
500 0 C
2
Flame temp
1780 0 C
3
Time required/heat
33 minutes
4
Fuel required
50 litres
5
Melting rate
400 kg/hr
6
Oxygen consumption
50 m3
7
Preheated air consumption
320 m3
Similarly maximum limit of output is shown in Table-5. Table-5: Maximum Limits of Output for Normalisation
Limits for Normalisation for Inputs Maximum limits of inputs for normalisation are shown in Table-4.
SN
Out put Output
Maximum limit
1
Specific fuel consumption
0.285 litre/kg 29
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TECHNICAL PAPER Normalised Values
z
The normalised values of input data selected for training and development of model as feed to ANN programme of MATLAB are shown in Table-6.
Table-6 : Normalised Values of Input Data of Model 2 Heat No.
Preheated Flame 0 Air TTemp emp emp.. ( C) Temp emp.. ( 0 C)
Time/ Heat (min.)
Fuel / He Heaa t (litr (litree s)
Melting Rate (kg/hr)
Oxygen/ Heat (m 3 )
Air/ Heat (m 3 )
1
0.848
0.9803
0.9696
0.960
0.9375
0.986
0.9968
2
0.874
0.9859
0.9696
0.930
0.9375
0.960
0.9906
3
0.896
0.9898
0.9545
0.916
0.9522
0.936
0.9781
4
0.930
0.9943
0.9393
0.900
0.9675
0.920
0.9687
5
0.940
0.9955
0.9242
0.892
0.9835
0.900
0.9656
6
0.948
0.9977
0.9212
0.858
0.9867
0.860
0.9281
7
0.952
0.9988
0.9121
0.832
0.9965
0.800
0.9187
The normalised values of output (specific fuel consumption) corresponding to inputs as per experimental data are given in Table-7.
Table-7 : Normalised Values of Output of Model 2 Heat No.
S p ecific FFuel uel Consumption lit/k g lit/kg
1
0.8420
2
0.8140
3
0.8035
4
0.7894
5
0.7824
6
0.7508
7
0.7298
Training and Development of Model – MATLAB Programme The ANN (Artificial Neural Network) programme contained in MATLAB is run as shown below—
%p12=[1745 1752 1755 1762 1770 1772 1773 1776 1778 1778]; %p13=[32 32 32 31.5 31 30.5 30.5 30.4 30.1 30.1]; %p14=[48 47 46.5 45.8 45 44.6 43.8 42.9 42 41.6]; %p15=[375 375 375 380.9 387 393.4 393.4 394.7 398.6 398.6]; %p16=[49.3 49 48 46.8 46 45 45 43 41.5 40]; %p17=[319 319 317 313 310 309 302 297 295 294]; %op=[0.2400 0.2600 0.2320 0.2290 0.2250 0.2230 0.2186 0.2140 0.2150 0.2080]; plot (p17,op) xlabel(‘Air/Heat........’); ylabel(‘Specific Fuel.....’);
Effect of Individual Input Parameter on Output (Specific Fuel Consumption) The effect of individual input parameter on output (specific fuel consumption) on basis of training and development of model is shown in following figures z
The Effect of Preheated Air on Specific Fuel Consumption – It is shown in Fig. 4.
clc; clear all; close all; %ip1=[424 437 448 465 470 474 476]; %ip2=[1745 1755 1762 1770 1772 1776 1778]; %ip3=[32 32 31.5 31 30.5 30.4 30.1]; %ip4=[48 46.5 45.8 45 44.6 42.9 41.6]; %ip5=[375 375 380.9 387 393.4 394.7 398.6]; %ip6=[49.3 48 46.8 46 45 43 40]; %ip7=[319 317 313 310 309 297 294]; %op= [0.240 0.232 0.229 0.225 0.223 0.214 0.208]; %p11=[424 430 437 448 465 470 472 474 475 476];
Fig. 4 : Effect of Preheated Air Temperature on Specific Fuel Consumption
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The Effect of Flame Temperature on Specific Fuel Consumption- It is shown in Fig. 5.
z
Fig. 8 : Effect of Melting Rate on Specific Fuel Consumption.
Fig. 5- Effect of Flame Temperature on Specific Fuel Consumption. z
The Effect of Time/Heat on Specific Fuel Consumption- It is shown in Fig. 6.
z
The Effect of Fuel/Heat on Specific Fuel Consumption – It is shown in Fig. 7.
Fig. 7 : Effect of Fuel/Heat on Specific Fuel Consumption
The Effect of Oxygen/Heat on Specific Fuel Consumption - It is shown in Fig. 9.
Fig. 9 : Effect of Oxygen/Heat on Specific Fuel Consumption (Model 2)
Fig. 6. : Effect of Time/Heat on Specific Fuel Consumption. z
The Effect of Melting Rate on Specific Fuel Consumption- It is shown in Fig. 8.
z
The Effect of Air/Heat on Specific Fuel Consumption – It is shown in Fig. 10.
Fig. 10 : Effect of Air/Heat on Specific Fuel Consumption (Model 2). 31
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TECHNICAL PAPER The output parameters (specific fuel consumption) during training of model are given in Table-8.
Table-8 : Output Parameters (Specific Fuel Consumption) After Training of Model 2. Heat No.
Modell p ecific FFuel uel Modellee d SSp Consumption (lit/kg of Model Model)
1
0.240
2
0.232
3
0.229
4
0.225
5
0.223
6
0.214
7
0.208
Test R un of Model -The Run model so trained and developed is being tested for its validity. The model is tested for all ten sets of observations as per Table-1.
Fig. 12 : Effect of Flame Temperature on Specific Fuel Consumption as per Test Run of Model 2. z
The Effect of Time/Heat on Specific Fuel consumption - It is shown in Fig. 13.
The Effect of Individual Input Parameter on Output (Specific Fuel Consumption) On basis of test running of model, the effect of individual input parameters on output (specific fuel consumption) is shown in following figures
z
The Effect of Preheated Air on Specific Fuel Consumption- It is shown in Fig.11.
z
Fig. 13 : Effect of Time/Heat on Specific Fuel Consumption as per Test Run of Model 2. z
The Effect of Fuel/Heat on Specific Fuel Consumption - It is shown in Fig. 14.
Fig. 11 : Effect of Preheated Air Temperature on Specific Fuel Consumption as per Test Run of Model z
The Effect of Flame Temperature on Specific Fuel consumption- It is shown in Fig. 12.
Fig. 14 : Effect of Fuel/Heat on Specific Fuel Consumption as per Test Run of Model.
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TECHNICAL PAPER z
The Effect of Melting Rate on Specific Fuel Consumption- It is shown in Fig. 15.
The output parameters (specific fuel consumption) of model 2 after test running are given in Table-9.
Table-9 : Output Parameters (Specific Fuel Consumption) of Model as per Test Running Heat No.
Fig. 15 : Effect of Melting Rate on Specific Fuel Consumption as per Test Run of Model. z
The Effect of Oxygen/Heat on Specific Fuel Consumption- It is shown in Fig. 16.
1 2 3 4 5 6 7 8 9 10
Modell p ecific FFuel uel Consumption Modellee d SSp Te st R g.) Run (lit/kg.) un of Model (lit/k 0.2400 0.2600 0.2320 0.2290 0.2250 0.2230 0.2186 0.2140 0.2150 0.2080
Comparison of Outputs The outputs (modelled specific fuel consumption) of above test run of model and the comparison with actual specific fuel consumption is shown in Table-10.
Results The error between actual and modelled specific fuel consumption varies from +0.18% to +10.6%. The average variation is 1.28%. It lies within the acceptable limits of ±10%.
Presentation of Error
Fig. 16 : Effect of Oxygen/Heat on Specific Fuel Consumption as per Test Run of Model. z
The Effect of Air/Heat on Specific Fuel Consumption- It is shown in Fig. 17.
Fig. 17 : Effect of Air/Heat on Specific Fuel Consumption as per Test Run of Model.
The error is presented graphically in Fig. 18 using MATLABclc; clear all; close all; x=[0 0.025 0 0 0 0 -0.0004 0 0.005 0]; y=erf(x) plot(y)
Fig. 18 : Error Graph of Model. 33
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TECHNICAL PAPER Table-10 : Comparison of Modelled and Experimental Specific Fuel Consumption of Model H e a t Preheated F l a m e No. Air Te m p . Temp emp.. ( 0 C) ( 0 C )
Time / Fuel / M e l t i n g Heat Rate Heat ( M i n u t e s ) ( l i t rree s ) ( k g / h r )
Oxygen A i r Modelled Cons/ S p ecific Cons/ H e a t ( m 3) H e a t ( m 3) F u e l (lit/kg)
Actual Absolute P e r c e n S p ecific E r r o r ta g e Fuel Error % (lit/kg.)
1
424.0
1745.0
32.00
48.0
375.0
49.3
319.0
0.2400
0.240
0.000
0.00
2
430.0
1752.0
32.00
47.0
375.0
49.0
319.0
0.2600
0.235
0.025
10.6
3
437.0
1755.0
32.00
46.5
375.0
48.0
317.0
0.2320
0.232
0.000
0.000
4
448.0
1762.0
31.50
45.8
380.9
46.8
313.0
0.2290
0.229
0.000
0.000
5
465.0
1770.0
31.00
45.0
387.0
46.0
310.0
0.2250
0.225
0.000
0.000
6
470.0
1772.0
30.50
44.6
393.4
45.0
309.0
0.2230
0.223
0.000
0.000
7
472.0
1773.0
30.50
43.8
393.4
45.0
302.0
0.2186
0.219
0.004
-0.18
8
474.0
1776.0
30.40
42.9
394.7
43.0
297.0
0.2140
0.214
0.000
0.000
9
475.0
1778.0
30.10
42.0
398.6
41.5
295.0
0.2150
0.210
0.005
2.38
10
476.0
1778.0
30.10
41.6
398.6
40.0
294.0
0.2080
0.208
0.000
0.000
Conclusions The average percentage error of model is 1.28%. The variations of both of these models are much lower than acceptable limits of ±10%. Hence, models are acceptable and further can be used for simulation.
Cupola Reactions –Behavior of Carbon, Silicon and Manganese, Transactions of AFS 1991, Vol.99, pp. 269-276. 5.
V. Sahajiwala and R.D. Pehlke, Experimental Investigations and Mathematical Modeling of Carbon Transport in a Cupola, Transactions of AFS 1992, Vol. 100, pp. 343-352.
6.
V. Stanek, S. Katz, C. F. Landefeld and M. E. Bauer, The AFS Cupola Process Model- A Computer Tool for Foundries, Modern Casting, June 1999, pp. 41-43.
7.
D.B. Karunakar, and G.L. Datta, Modeling of Cupola Furnace Parameters Using Artificial Neural Networks, Indian Foundry Journal, Vol. 48, No. 5, May 2002, pp. 29-39.
8.
Christopher M. Bishop, Neural Networks for Pattern Recognition, Oxford University Press, Sixth Indian Edition pp. 116-119.
9.
Symon Haykins, Neural Networks, Pearson Prentice Hall, pp. 139197.
References 1.
W.W. Levis, Variables Affecting Carbon Control in Cupola, Transactions of AFS 1947, Vol. 55, pp. 626-632.
2.
R.D. Pehlke, Thermo-Chemical Model of Computer Prediction of Cupola Performance, Transactions of AFS 1963, Vol. 71, pp.580-587.
3.
C. F. Landefeld and S. Katz, A Dual Stream Model of Carbon Pickup based on Carbon Activity, Cast Metals ,1976, Vol. 3, pp.163-17.
4.
V. Sahajiwala, R.D. Pehlke, C. F. Lardefeld and S. Katz, Modeling Key
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