CHAPTER 10 VALIDATION OF TEST WITH ARTIFICAL NEURAL NETWORK

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1 175 CHAPTER 10 VALIDATION OF TEST WITH ARTIFICAL NEURAL NETWORK 10.1 INTRODUCTION Amongs he research work performed, he bes resuls of experimenal work are validaed wih Arificial Neural Nework. From he experimenal observaion, he bes resul of he fuel was found o be POME and is blends wih diesel as fuel. For beer validaion, he fuel performance like specific fuel consumpion and brake hermal efficiency of diesel engines are validaed wih ANN DEVELOPMENT OF NEURAL NETWORK MODEL ANN is one of he mos powerful compuer modeling echniques based on saisical approach, currenly being used in many fields of engineering for modeling complex relaionships which are very difficul o describe wih physical models. The aracion of neural neworks comes from heir remarkable informaion, processing characerisics perinen mainly o non-lineariy, high parallelism, faul and noise olerance and learning and generalized capabiliy. There has been a coninual increase in he research owards he applicaion of arificial neural neworks in modeling and monioring of performance of CI engine. The objecive of he sudy was o develop an ANN model o predic he performances in palm oil mehyl eser diesel blends (Kiani e al. 2010).

2 Muli Layer Feed Forward Neural Nework The muli-layer nework archiecure has one inpu layer, one oupu layer and also has one or more inermediary layers, called hidden layers. The compuaion unis of hidden layer are known as hidden neurons. The hidden layer aids in performing useful inermediary compuaions before direcing he inpu o he oupu layer. The inpu layer neurons are linked o he hidden layer neurons and he corresponding weighs are referred o as inpu-hidden layer weighs. The hidden layer neurons are again linked o he oupu layer neurons and he corresponding weighs are referred o as hidden-oupu layer weighs. A muli-layer feed forward nework wih n 1 inpu neurons, m 1 neurons in he oupu layer and n 2 oupu neurons is wrien as n 1 - m 1 - n Back Propagaion Nework I is a sysemaic mehod for raining muli-layer arificial neural neworks. I uses gradien descen algorihms and he erm back propagaion refers o he way in which he gradien is compued for non-linear neworks. The algorihm allows experimenal acquisiion of he inpu/oupu mapping knowledge wihin mulilayer neworks. Back propagaion akes place in hree sages. 1. Feed forward of he inpu raining paern 2. Back propagaion of he associaed error 3. Weigh adjusmen During feed forward, each inpu neuron receives an inpu signal and broadcass i o each hidden neuron which in urn compues he acivaion and passes i on o each oupu uni which again compues he acivaion o obain he ne oupu. During raining, he ne oupu is compared wih he arge value and appropriae error is calculaed. From he error, he error facor is obained

3 177 which is used o disribue he error back o he hidden layer. The weighs are updaed accordingly. In a similar manner, he error facor is calculaed for all he unis. Afer he error facors are obained, he weighs are updaed simulaneously Nework Learning Rule for Back Propagaion A neuron is considered as an adapive elemen. The weigh of he neuron is modified depending on he inpu signal i receives and is oupu value and he associaed eacher s response. In some cases, if he eacher signal is no available, he neuron will modify he weigh based on inpu and/or oupu (Zurada, 1997). In general learning, he weighs ha are conneced o he i h neuron is given by Equaion (10.1) W i = [W 1i, W 2i, W 3i W ji. W ni ] T (10.1) The weigh vecor increases in proporion o he produc of inpu X and learning signal r. The learning signal for he dela learning rule is defined by he following Equaion (10.2) r i i i (10.2) The erm f (w i x) is he derivaive of he acivaion funcion f (w i x) and d i is he eacher signal. The dela learning rule for he neural nework model is shown in Figure The learning rule can be readily derived from he condiion of leas squared error beween O i and d i where O i is he prediced value. The gradien vecor wih respec o W i of he squared error E is given by Equaion (10.3) E i i (10.3)

4 178 This is equivalen o 1 E d - f(w X) 2 i i 2 (10.4) The error gradien vecor value is obained as E d O f ' (W X)X i i i (10.5) The componens of he gradien vecor are E d O f ' (W X)X forj 1,2...n (10.6) W i i i j ij The minimizaion of he error requires he weigh changes o be in he negaive direcion, Hence, i (10.7) Where Therefore ' i i i i (10.8) For single weigh he adjusmen becomes ' ij i i i j (10.9) raining. Hence, he weighs can be iniialized a any values for his mehod of

5 179 Figure 10.1 Dela learning rule ANN Model for Performance Characerisics The procedure for he developmen of neural nework model is shown in Figure The four seps used in he developmen of he ANN model for specific fuel consumpion and brake hermal efficiency are as follows: i) Collecion of inpu/oupu daa se; ii) Preprocessing of inpu/oupu daa se; iii) Neural nework designing and raining; iv) Tesing of he nework;

6 180 Sar Impor he daa from workspace Provide properies for he nework (ype, number of layers and raining, adapion learning, performance and ransfer funcions) Number of neurons in hidden layer is 10 Train he nework Compare resuls of five neworks Expor he resuls of he bes nework Sop Figure 10.2 Seps involved in he developmen of neural nework model

7 Collecion of inpu and oupu daa se The inpu parameers used o rain he nework consiss of four neurons for he engine process parameers B, r, L and m w. The oupu parameer used o rain he nework has wo neurons, i.e. SFC and BTE Preprocessing of inpu and oupu daa se dependen on The generalizaion capabiliy of he neural nework is essenially 1. The selecion of appropriae inpu/oupu parameers of he process. 2. The disribuion of daa se. 3. The forma of presenaion of daa se o he nework. nework model. In oal, 30 experimenal daa were colleced for building he neural Neural nework designing and raining The experimenal daa were o be separaed ino raining and esing daa. There were no general guidelines available which could be followed o measure he raio beween he amoun of raining and esing samples. As per he recommended raio of raining and esing, his can be given in percenage such as 90%: 10%, 85%: 15%, 80:20% and 70%: 30%. Hence ou of 30 experimenal daa 70% was used for raining, 15% for esing and 15% for validaion. So he recommended amouns of raining, esing and validaion samples were 20, 5 and 5 respecively. The inpu and oupu daa for he raining, esing and validaion samples are shown in Table 10.1.

8 182 Table 10.1 Design marixes for an ANN model wih measured value and prediced value of performance parameers S. No. Design marix Performance of measured values Performance of Prediced values V r L wf SFC BTE SFC BTE (kg) (ml/s) (kg/kwhr) (%) (kg/kwhr) (%)

9 183 The nex sep was o decide he suiable nework srucure for SFC and BTE. The nework srucure was usually designed based on rial and error. The process of rial and error was carried ou by adjusing he number of nodes of hidden layer of he nework srucure. Though i was free o check he nework wih any number of nodes in he hidden layer, however i was subjec o he complexiy of he mapping, compuer memory, compuaion ime and he desired daa conrol effec. If oo many nodes were used i may resul in wase of compuer memory and compuaion ime, while few nodes may no provide he desired daa conrol effec. Hence, he rial and error in his sudy were limied o one nework, which is The neworks were creaed in MATLAB 7.6. The nework archiecures are shown as Figure Figure 10.3 Nework archiecure showing en neurons in he hidden layer The raining of he nework was done by Levenberg Marquard (LM) algorihm. The Levenberg Marquard algorihm was designed o approach second order raining speed wihou having o compue he Hessian marix. When he performance funcion has he form of a sum of squares (as is ypical

10 184 in raining feed forward neworks) hen he Hessian marix can be approximaed as T H J J (10.10) Where H is he Hessian marix, he gradien can be compued as T g J e (10.11) Where J is he Jacobian marix ha conains firs derivaives of he neworks wih respec o he weighs and biases, e is a vecor of nework errors. The Jacobian marix can be compued hrough a sandard back propagaion echnique ha was much less complex han compuing Hessian marix. The Levenberg Marquard algorihm uses his approximaion o he Hessian marix using Equaion. X k 1 X K T J J 1 T J e (10.12) When X k 1 X K T J J 1 T J e. (10.13) The above equaion represens Newon mehod. This is faser and descen wih a small sep size. Hence, o move owards Newon s mehod o was decreased afer each successful sep (reducion in performance funcion) and was increased only when a enaive sep increases he performance funcion. In his way, he performance funcion was always reduced a he end of he corresponding ieraion of he algorihm. Hence, his algorihm appears o be a faser mehod for raining moderae-sized

11 185 feed forward neural neworks up o several hundred weighs (Mah Work Inc., 2008). During raining, he inpus o he neurons were modified wih approximae weigh. The sum of he modified weigh inpu and bias was hen modified by a an sigmoid ransfer funcion. Similarly, oupu from he las hidden layer was modified by an appropriae weigh and hen he sum of modified oupu signal was again modified by a an sigmoid ransfer funcion. The final oupu was colleced a he oupu layer Tesing of he nework Only one nework was esed o deermine he performance of he ANN model for predicing performance parameers. During raining, each ime a se of inpus X i of a raining sample was presened and he corresponding oupu O i (prediced values) was obained. The prediced value of he nework model was compared wih he acual value (d i ). The comparison was done by calculaing he mean sum of he squared error (MSE) beween d i and O i given in Equaion (10.13). MSE (d O ) 2 (10.14) i i The objecive of he algorihm was o minimize he mean sum of squared error for he enire experimenal daa RESULTS AND DISCUSSIONS Figure 10.4 shows he performance and error graph of SFC and BTE of nework The nework was rained for 174 ieraions and he bes validaion performance was I was obained a 174 epochs. The error percenage of his nework is in he range of -0.45% o 0.50%. This is shown in Figure 10.5 and 10.6.

12 186 Figure 10.4 Performance graph of nework Figure 10.5 Error graph of nework

13 187 Figure 10.6 Error graph of nework I is observed ha a prediced value of specific fuel consumpion and brake hermal efficiency was obained for raining, esing, and validaion of all he daa. The percenage error was wihin he limis of 0.05%. Hence here exiss a close relaionship beween he experimenal and prediced values. This indicaes ha he nework is suiable for he predicion of engine performance parameers of specific fuel consumpion and brake hermal efficiency VALIDATION OF RESULTS Confirmaory ess were conduced wih he same experimenal seup o validae he accuracy of he resuls obained. The resuls of confirmaory ess are presened in Table 10.2.

14 188 Table 10.2 Resuls of confirmaory ess Tes No Process Parameers OV PV B r L m w (ANN SFC BTE model) Specific fuel consumpion % Error Brake hermal efficiency PV (ANN model) % Error Mean Error OV is observed value and PV is prediced value of performance parameers. From he confirmaory ess, i was found ha he ANN model were able o predic he performance parameers wih high accuracy (Amarnah and Prabhakaran, 2012) SUMMARY This chaper has discussed he developmen of he ANN model for predicing performance of diesel engines. I has been found in he analysis of neural neworks ha he performance of he nework highly depends on he number of neurons in he hidden layer. This chaper discussed he performance of single nework which had differen neurons in he hidden layer. From he analysis, he nework which had high accuracy in predicing SFC and BTE was idenified. The models developed o predic he performance characerisics have high accuracy. This has been validaed by conducing confirmaory ess. The direc and ineracive effecs of he process parameers were presened in graphical form. This helped o undersand he behavior of he process parameers on performance characerisics. The algorihm which produced he accurae resul was idenified.