30120140502002 2

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30120140502002 2

  1. 1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING 6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 2, February (2014), pp. 08-16, © IAEME AND TECHNOLOGY (IJMET) ISSN 0976 – 6340 (Print) ISSN 0976 – 6359 (Online) Volume 5, Issue 2, February (2014), pp. 08-16 © IAEME: www.iaeme.com/ijmet.asp Journal Impact Factor (2014): 3.8231 (Calculated by GISI) www.jifactor.com IJMET ©IAEME EXTRACTION OF NUMERICAL MODEL THROUGH OPTIMIZATION OF ANN MODEL FOR MANUALLY DRIVEN BRICK MAKING MACHINE Mr. P. A. Chandak1, 1 Mr. J. P. Modak2 Asst. Professor, Mechanical Engineering, DMIETR, Wardha, India Emeritus Professor, Mechanical Engineering, PCE, Nagpur, India 2 ABSTRACT Considerable research work is carried in development of process units energized by Human Powered Flywheel Motor (HPFM). The process units tried so far are mostly rural based [12] such as wood turning, wood strip cutting, electricity generation, low head water lifting, etc. The HPFM comprises of three subsystems namely (i) HPFM, (ii) Torsionally flexible clutch and (iii) A Process Unit. Brick making is one of the processes and experiments were conducted to model the system in order to enhance its productivity. The experimental data based mathematical model was also formulated for the system, but the model could not predict the experimental findings accurately and precisely. The present research work utilizes artificial neural network (ANN) technique for modelling of brick making process. The author applies an exhaustive optimization technique which could be used for almost all applications under ANN modelling and emerges with unmatched result. The document extracts the mathematical model through optimized ANN model for the projected process of manufacturing of bricks and compares prediction through it. This technique of development of mathematical model could be engaged in future for production of controllers based on linear electronic circuit, microprocessor, etc. The article compares the predictions of experimental findings through previous empirical and ANN based mathematical model as well, enlightening the strength of ANN Modelling. Key Words: MATLAB, ANN Modelling, Mathematical Modelling, ANN parameters, etc. 8
  2. 2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 5, Issue 2, February (2014), pp. 086359(Online), -16, © IAEME 1. INTRODUCTION TO MANUALLY DRIVEN BRICK MAKING MACHINE riven 1.1. Working of Manually Driven Brick Making Machine A manually driven Auger-type brick making [1] [2] [9] [10] machine developed by Dr. J. P. type [ Modak is as shown in figure. The operator drives the flywheel (17) though chain (25) and a pair of gears (19, 20). The chain drive is utilized for first stage transmission because the drive is required to be irreversible. This is achieved with the conventional bicycle drive with a free wheel (21). When the ieved flywheel attains sufficient speed, the single jaw clutch (13, 15) is engaged. The clutch drives the auger screw through a pair of gears (9, 10). The mix fed through hopper (3). A cone (2) connects the cone drum (30) to the die (1). The cone eliminates the rotary motion of the mix before it enters the die. The extracted column is collected in a detachable mould (4). It is lined on the inside by Perspex to provide least resistance to motion of the column. The column is subsequently demoulded by placing it upside down on the platform. The mould is moved horizontally, leaving the column on the platform. About one or two hours after the column is laid on the platform, it becomes stiff enough to be cut by a cutter to form bricks of standard size. 1. DIE, 2. CONE, 3. HOPPER, 4. AL MOULD, 5. MOULDING STAND, 6. CONVEYOR SCREW, 7. CONVEYER SHAFT, 8. HOPPER, 9. GEAR, 10. PINION, 11. PINION SHAFT, 12. BEARING, MOVABLE HALF CLUTCH, 14.CLUTCH LEVER, 15.FIXED HALF CLUTCH, 16.FLYWHEEL SHAFT, 17.FLYWHEEL, 18, BEARING FOR FLYWHEEL, 19. PINION II, 20. GEAR II, 21. FREWHELL, 22. INTERMEDIATE SHAFT, 23. BEARING FOR INTERMEDIATE SHAFT, 24. CRANK GEAR, 25. PINION FOLLOWER CHAIN, 26. DRIVER SEAT, 27. HANDLE, 28. BRACKET, 29. FRAME, 30. CONVEYOR DRUM. Fig. 1. Manually Driven Brick Making Machine [1] 9
  3. 3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 2, February (2014), pp. 08-16, © IAEME Following process variables were involved in experimentation. variables is tabulated in Table I. TABLE I. Sr No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Symbols and type of PROCESS VARIABLES WITH THEIR SYMBOLS [1] Description of variables Type of variable Symbol Dimension Weight of lime Weight of sand Weight of flyash Weight of water Outside diameter of screw Inside diameter of screw Pitch of Screw Larger Diameter of Cone Smaller Diameter of Cone Length of cone Length of die Moment of Inertia of flywheel Angular velocity of flywheel Acceleration of due to gravity Gear ratio Length of square side of die Strength of brick Length of Extruded Brick Column Time of Extrusion Maximum length of Extruded Brick Column Pressure of Extrusion Critical Instantaneous Torque on the angular shaft Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Independent Dependent Dependent Dependent Dependent Dependent WL Ws Wf Ww D1 D2 P D1 D3 LC LD I W G G S Sb Lb Te Lbm Pc ML-1T-2 ML-1T-2 ML-1T-2 ML-1T-2 L L L L L L L ML2 T-1 LT-2 L ML-1T-2 L T L ML-1T-2 Dependent T ML-1T-2 1.2. Experimental observations and Empirical Model The experimental observations [1] were recorded in tabulated form. As the variables involved were high in number dimensionless pi terms were evaluated. And an empirical model was generated to predict the experimental findings. The model was as follows [1]. ‫ 1ܦ / ܾܮ‬ൌ 0.0043 ሺ‫1ܦ/ܦܮ‬ሻ െ 1.8091 ‫ כ‬ሺ‫݂ܹ݃ܫ/21ܦ‬ሻ 0.139 ‫ כ‬ሺ‫ܩ‬ሻ 0.2766 ‫ כ‬ሺ√ ‫ܹ .݃/1ܦ‬ሻ 1.27 ‫ כ‬ሺ‫1ܦ/ܿܮ‬ሻ െ 1.977 ‫ כ‬ሺܲ/ ‫1ܦ‬ሻ1.3075 ‫ כ‬ሺ‫1ܦ / 2ܦ‬ሻ0.8313 ……… (1) [2] The above equation (1) was derived through traditional methods of modelling and found unsatisfactory in prediction of experimental findings. This limits its further application in development of controller for the machine system. Hence it is required to adapt new modelling technique which could give better and satisfactory results in prediction of experimental and unseen data. The paper utilizes ANN modelling technique for modelling of machine system and emerges with inimitable solution to above defined problem. 10
  4. 4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 2, February (2014), pp. 08-16, © IAEME 2. MODIFICATIONS IN THE DATABASE The experimental evidences developed during experimentation were very little in number. As a result experimental database was found to be insufficient for training and validation of the model generated though ANN simulation. In order to develop ANN model, the existing database was modified and improved in magnitude by maneuvering plots on the basis of present experimental evidences. The intermediate positions in the plot are positioned and noted [6]. This database generated is as follows. TABLE II. Sr. No. 1 ↓ 240 ↓ 550 ↓ 710 ↓ 912 ↓ 1555 MODIFIED DATA [11] [3] Independent Variables LD/D1 0.2 ↓ 0.5 ↓ 0.5 ↓ 0.5 ↓ 0.5 ↓ 0.5 D12/Ig.Wf 3.7 ↓ 2.10 ↓ 3.7 ↓ 3.7 ↓ 3.7 ↓ 3.7 G 4.5 ↓ 4.5 ↓ 2.8 ↓ 4.5 ↓ 4.5 ↓ 4.5 √(D1/g).W 9.19 ↓ 9.19 ↓ 9.19 ↓ 2.84 ↓ 9.19 ↓ 9.19 Lc/ D1 0.5 ↓ 0.5 ↓ 0.5 ↓ 0.5 ↓ 0.43 ↓ 0.5 P/ D1 0.24 ↓ 0.24 ↓ 0.24 ↓ 0.24 ↓ 0.24 ↓ 0.24 D2 / D1 0.4 ↓ 0.4 ↓ 0.4 ↓ 0.4 ↓ 0.4 ↓ 0.39 Dependent Variables Lb / D1 1.174 ↓ 0.854 ↓ 1.455 ↓ 0.203 ↓ 0.995 ↓ 1.157 3. ARTIFICIAL NEURAL NEWORK (ANN) PARAMERS INVOLVED IN MODELLING Important ANN Parameters [4] [5] [6] involved in modeling through artificial neural network are as follows • • • • • • • • Network Topology Number of Layers in the network Number of Neurons Learning Algorithm Training Methods Activation functions/ Transfer Functions used Type of Networks Performance function 4. OPTIMIZATION THROUGH DISCIPLINED MODIFICATION OF ANN PARAMETERS The ANN parameters are sequentially modified as shown in table III and prediction through each model is examined through their plots. Every parameter posses its diversified standard values out of which some are chosen and their effects are observed after and during training. The table III shows the program number and respected value of each parameter. For each case of a program one parameter is varied and other parameters were allocated some constant standard value. 11
  5. 5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 2, February (2014), pp. 08-16, © IAEME Program Number P1 P2 P3 P4 P5 P6 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 TABLE III. SEQUENTIAL MODELLING EVALUATION [4] Types of transfer Type of function Hidden Training Performance layer Size 20 100 200 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 Function trainlm trainlm trainlm trainb trainbfg trainbr trainlm trainlm trainlm trainlm trainlm trainlm trainlm trainlm trainlm trainlm trainlm trainlm trainlm trainlm Function mse mse mse mse mse mse mae sse sse sse sse sse sse sse sse sse sse sse sse sse Layer1 logsig logsig logsig logsig logsig logsig logsig logsig tansig logsig logsig logsig tansig tansig logsig logsig logsig logsig logsig logsig Layer2 purelin purelin purelin purelin purelin purelin purelin purelin purelin purelin hardlim tansig logsig satlin satlin poslin tansig tansig tansig tansig Type of Learning Algorithm learngd learngd learngd learngd learngd learngd learngd learngd learngd learngd learngd learngd learngd learngd learngd learngd learncon learngd learnh learnk It is not possible to include all the graphs generated for each program because of limitations of the paper. Hence some of them are shown to understand the methodology of optimization. Fig. 2. Percentage error with 100 Neurons [4] 12
  6. 6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 2, February (2014), pp. 08-16, © IAEME Fig. 3. Percentage error with training Function “trainlm” [4] Fig. 4. Percentage error with performance Function “sse” [4] Fig. 5. Percentage error with layer transfer Function “logsig, tansig” [4] 13
  7. 7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 2, February (2014), pp. 08-16, © IAEME Fig. 6. Percentage error with Learn Function “learncon” [4] 5. EXTRACTION OF NUMERICAL MODEL The optimized network has specific values of ANN parameters assigned to it. The network architecture [7] (fig7) shows the mathematics involved [5]. Fig. 7. Architecture of Artificial Neural Network for the optimized network. The numerical model extracted through optimized ANN model is as follows. ܱ‫ ݐݑ݌ݐݑ‬ൌ ‫݈݊݅݁ݎݑ݌‬ሺ‫ כ ܹܮ‬ሺ‫݃݅ݏ݊ܽݐ‬ሺ‫ ܾ כ ܹܫ‬൅ ‫ܾܫ‬ሻሻ ൅ ܱܾሻ Where, LW = Weight Matrix of Output layer of AN IW = Weight Matrix of Input layer of ANN Purelin = Function of Output layer of ANN ……….(2) Ob = Bias Matrix of Output Layer of ANN Ib = Bias Matrix of Input Layer of ANN Tansig = Function of input layer of ANN The above equation (2) [8] gives numerical statement for optimized ANN model for which the transfer functions are ‘tansig’ and ‘purelin’ assigned to input and output layer respectively. IW and LW are weight matrices multiplied respectively to input vectors of input layer and output layer. Transferring the above product matrix through transfer function gives output of each layer. The output of input layer becomes input for output layer. 14
  8. 8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 2, February (2014), pp. 08-16, © IAEME Fig. 8. Prediction of experimental findings with optimized ANN model The comparative analysis (fig 7) shows the close curves among the experimental findings and its predication though the numerical model. Fig. 9. Percentage error in prediction through optimized ANN model 6. CONVERSATION ON RESULTS • • • • • As the neuron size is amplified, error in prediction of experimental results decreases while higher neuron size leads to higher training time. Training styles have great influence on performance of the network. Hence it is to be picked appropriately. Performance function has little effect on prediction but wants to observe. Transfer functions plays key role in output of ANN model. Each layer has to assign a transfer function independently and their combination results to overall outcome. The numerical model developed gives very good results in prediction of experimental data. 15
  9. 9. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online), Volume 5, Issue 2, February (2014), pp. 08-16, © IAEME 7. CONCLUSION The paper is illustrating methodology of optimization of ANN model and developing a numerical model through ANN modelling. This model has great affinity towards development of controller based on numerical model. Hence this method may be used in many of the application where researchers are striving to atomize any of the process fully or partially. 8. REFERENCES JOURNAL PAPERS: [1] [2] [3] [4] Modak J P and Askhedkar R D “Hypothesis for the extrusion of lime flash sand brick using a manually driven Brick making machine”, Bulding Research and Information U.K., V22, N1, Pp 47-54, 1994 Modak J P and Bapat A R “Manually driven flywheel motor operates wood turning machine”, Contempory Ergonomics, Proc. Ergonomics Society annual convension 13-16 April, Edinburg, Scotland, Pp 352-357, 1993. Chandak P A, Modak J P, “Optimization of artificial neural network model for improvement of artificial intelligence of manually driven brick making machine powered by HPFM”, International Journal of Chaos, Control Modelling and Simulation, Vol 2, No 3, Sep 2013. Chandak P A, Lende A R, Modak J P, “A literature review on Methodology & Fundamental of Development of mathematical model through Simulation of artificial neural network”, International journal of computer application, Vol 4, issue 1, to be published, 2014. BOOKS: [5] [6] [7] [8] S. N. Shvanandam, “Introduction to Neural Network using Matlab 6.0”, McGraw Hill publisher. Stamtios V. Kartaplopoulos , Understanding Neural Networks and Fuzzy Logics, IEEE Pres. Neural Network Toolbox TM 7 User’s Guide R2010a, Mathworks.com Rudra Pratap, “Getting Started with Matlab7,” Oxford, First Indian Edition 2006. THESIS: [9] A. R. Bapat, “Experimental Optimization of a manually driven flywheel motor”, M.E. Thesis, VNIT, Nagpur. [10] A. R. Bapat, “Experimentation of Generalized experimental model for a manually driven flywheel motor”, PhD Thesis, VNIT, Nagpur. [11] P. A. Chandak.”Modelling of Manually driven brick making machine through Artificial Neural Network”, M. Tech. Thesis, PCE, Nagpur, 2007. PROCEEDINGS: [12] Modak J P, “Human powered flywheel motor, Concept, Design, Dynamics and Applications”, International Federation for the promotion of Mechanism and Machine Science, IFToMM, Proceedings of World Congress, 1987. 16

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