neural network for the prediction of retrofitting ......cnc system refers to the automation of...

Neural Network for the Prediction of Retrofitting/Reconditioning/Upgradation

cost of CNC Machines BHUPENDRA MISHRA

ENGINEER, BHEL BHOPAL E-Mail- [email protected]

172-A Sector-A Awadhpuri Opposite SBI Awadhpuri

BHEL Bhopal -462021 M.P. INDIA

Abstract

The main objective of this paper is to predict the Retrofitting/Reconditioning/Upgradation cost of used CNC Machines in manufacturing industries so as to optimize the capital investments on these activities. I find that neural network can be used to predict these costs, as there is no known relationship between the cost under consideration and the factors responsible for the retrofitting/reconditioning/upgradation. Although few replacement model based on depreciation value of the CNC Machine, but this model fails to account the effect of technological obsolescence, mechanical condition of the machine and the substantial change in the production technology and valid only for the capital retirement, but not able to determine the Retrofitting/Reconditioning/Up-gradation projects and their costing.

Keywords: Neural Network; CNC; Machine; MTTR; MTBF; OEE; prediction; back-propagation; retrofitting; reconditioning; up gradation; technological obsolescence; MSE

1. Introduction

CNC system refers to the automation of machine tools that are operated by abstractly programmed commands encoded on storage medium, as opposed to manually controlled. In Manufacturing sectors like power equipment manufacturing, automobiles, process industry etc CNC System based machines are used for various cutting applications like drilling, milling, turning, boring, punching, notching and for special purposes like winding, pressing, taping etc. Due to the ageing of the machine, technological obsolescence, reduced accuracy, increased number of breakdown make it necessary to think for the Retrofitting/Reconditioning/Upgradation of the machine, but there is no widely accepted model for the estimation of cost of retrofitting/reconditioning/upgradation. Presently the practice is to do the costing based on salvage value of the machine based on depreciation and other financial factors but it completely neglects the factors mechanical condition of the machine, technological obsolescence of the control system, ratio of estimated life of the machine after retrofitting and life of a new machine. To incorporate these factors and to find out how these factors affect the cost of retrofitting, I uses neural network with following inputs

1. Cost of Similar type of new Machine 2. Age of the machine under consideration (in years) 3. Estimated age of the Machine after retrofitting/Reconditioning/Upgradation done (typically 2-10 years) 4. Age of the New Machine if procured (in years) 5. Availability of the machine (based on MTTR,MTBF,OEE,% breakdown in specified time) 6. Control system is presently manufactured by OEM or Not. 7. Spares of the Control system and other Parts are provided by OEM or not.

Bhupendra Mishra et al. / International Journal of Engineering Science and Technology (IJEST)

ISSN : 0975-5462 Vol. 3 No.10 October 2011 7316

8. Mechanical condition of the machine (determined by Geometrical Accuracy tests and Laser positioning Accuracy tests.

9. Substantial Change in the production technology.

My work differ from the previous works in the way that I try to use the multi-variable non-linear neural network so that i can incorporate all the responsible parameters in the same model to find out the cost.

In the next section I present the Data used in my study, while the various types of models are discussed in section 3. In section 4 we compare the prediction accuracy of each model and conduct performance test of significance. The final section concludes and suggests avenues for further research.

2. Data

The Data is collected from the various manufacturing industries in India including Power Equipment Manufaturing Industries, Sugar Industries, Automobiles Industries. Data Compiled for more than 700 CNC Machines, out of which more than 300 CNC upgradation/retrofitting/reconditioning projects are completed and the data of these projects is the basis of training samples to the neural network. The machines from 1970-2011 are covered in this data. In addition to the above data I assume few data which seems to be obvious like if i recently procured a machine, in no case I will go for a retrofitting/reconditioning/upgradation option because my machine cost is still not recovered, another one is like if the retrofitting/reconditioning/upgradation cost is greater than the cost of similar type of new machine it will not go for retrofitting/reconditioning/upgradation. Further Details on the data can be found on Appendix –A

3. Models

In this section I present the neural network model which is used for the prediction of retrofitting/reconditioning/upgradation cost of CNC machines. I used multilayer neural network with either two hidden layer h1 and h2 or single hidden layer h1, number of neurons in the layers h1 and h2 will be determined by the Training performance of the network. Activation Functions used for layer h1 is ‘linear function’ and for layer h2 is ‘tan sigmoid’.

3.1 Basic Neural Network Architecture An Artificial neural network consists of a pool of simple processing units which communicate by sending signals to each other over a large number of weighted connections. Fig1 Shows the single layer neural network. Fig 2 & 3 shows the most commonly used activation functions.

Fig 1: Single Layer Neuron Model



Fig2 : Tan Sigmoid Activation Function Fig3 : Linear Activation Function

∑ , . (1)

) (2)

Where f denotes the activation function of the network

3.2 Network Topologies 3.2.1 Feed Forward Network

In this network the data flow from input to output units is strictly feed forward. The data processing can extend over multiple (layers of) units, but no feedback connections are present, that is, connections extending from outputs of units to inputs of units in the same layer or previous layers. Fig 4 shows the feed forward neural network

Fig 4: Multilayer Feed Forward Neural Network

3.2.2 Recurrent Networks

This type of network contains feedback connections. Contrary to feed-forward networks, the dynamical properties of the network are important. In some cases, the activation values of the units undergo a relaxation process such that the network will evolve to a stable state in which these activations do not change anymore. In other applications, the change of the activation values of the output neurons is significant, such that the dynamical behavior constitutes the output of the network (Pearlmutter, 1990). Examples of recurrent networks have been presented by Anderson (Anderson, 1977), Kohonen (Kohonen, 1977), and Hopfield (Hopfield, 1982)



Fig 5: Hopfield Recurrent Neural Network

3.3 Training of Neural Networks 3.3.1 Paradigms of Learning

The neural network models used in this paper are broadly classified into two categories 1. Supervised Feed forward neural network with single hidden layer. 2. Supervised Feed forward neural network with two hidden layers. Approach 1: Supervised Feed Forward network with single hidden layer. Here the neural network is tested with number of neurons in hidden layer from 1 to 20, Activation Function Used here for 1st Hidden layer is ‘tansig’ and the performance parameters are tabulated, results of which are shown in next section.. Approach 2: Supervised Feed Forward network with two hidden layers. Here the neural network is tested with number of neurons in first hidden layer from 1 to 20 and number of neurons in second hidden layer from 1 to 10 Activation function used for 1st layer is ‘purelin’ and for 2nd layer is ‘tansig ’and the performance parameters are tabulated, results of which are shown in next section.

3.3.2 Delta Rule

The error function, as indicated by the name least mean square, is the summed squared error. That is, the total error E is defined to be

∑ ∑ ² (3)

Where is the mean square error in kth pattern of the input dk is the desired output of ‘k’ pattern Ok is the output we get from the neural network for pattern ‘k’ Xj is the input jth neuron Wj is the connection weight between unit j and output unit.

The LMS procedure finds the value of all the weights that minimizes the error function by a method called Gradient descent. The idea is to make the change in weight proportional to the negative of the derivative of the error as measured on the current pattern with respect to each weight



(4)

(5)

(6)

(7)

(8)

Levenberg-Marquardt (trainlm)

Like the quasi-Newton methods, the Levenberg-Marquardt algorithm (1963) was designed to approach second-order training speed without having to compute the Hessian matrix. When the performance function has the form of a sum of squares (as is typical in training feedforward networks), then the Hessian matrix can be approximated as

(9)

and the gradient can be computed as

(10)

where is the Jacobian matrix that contains first derivatives of the network errors with respect to the weights and biases, and e is a vector of network errors. The Jacobian matrix can be computed through a standard backpropagation technique (see [HaMe94]) that is much less complex than computing the Hessian matrix.

The Levenberg-Marquardt algorithm uses this approximation to the Hessian matrix in the following Newton-like update:

(11)

When the scalar µ is zero, this is just Newton's method, using the approximate Hessian matrix. When µ is large, this becomes gradient descent with a small step size. Newton's method is faster and more accurate near an error minimum, so the aim is to shift towards Newton's method as quickly as possible. Thus, µ is decreased after each successful step (reduction in performance function) and is increased only when a tentative step would increase the performance function. In this way, the performance function will always be reduced at each iteration of the algorithm.

I present only the prediction results for the best models, since we want to ensure that the performance of neural networks is not overstated. The models presented are the products of an extensive specification search that focus on minimizing the out-of-sample Mean Squared Error (MSE) over the test sample so as to not to bias our results. The Back-propagation algorithm is used to train the neural network and may require several hundreds of thousands of passes through the data during the search procedure to meet the pre-specified convergence criterion. A neural network would be optimized using data from 1980 to 2011 and the performance parameters are recorded for every model.



3.4 System and Methods

The Classical Investment literature assume that capital is homogeneous, lives forever and has a constant depreciation rate which is unrelated to economic and technological conditions. When Capital is heterogeneous it is difficult to believe that depreciation is constant and exogenous. As discussed in an early literature by Feldstein and Rotschild (1974) and Feldstein and Foot (1971), a constant depreciation with differing rates across goods can create lumpiness in investment and echoes of past investment in future decisions. Boddy and Gort (1971) noted early that there is an evidence of capital heterogeneity across sectors and more recent work by Goolsbee and Gross (1997) has demonstrated how important capital heterogeneity is for the study of investment at the micro level.

In the area of capital retirements, recent advances in macroeconomics have shown that in capital models with embodied technological process, the depreciation and obsolescence of capital become economic decisions rather than consequences of the physical delay. Firms must decide when it makes sense to retrofit/reconditioned/upgrade/replace the old machine and how much cost can be invested in this activity.

In the view of above, the first step is to find out all the parameters that affect the cost of retrofit/reconditioned/upgrade/replace. To do this I divide all the responsible parameters into two categories

1. Parameters that count for financial factors 2. Parameters that count for technology and productivity factors 1. Parameters that count for financial factors

1.1 Cost of similar type of new machine (if replacement of capital is done in case of retirement of existing capital)

1.2 Age of the machine under consideration (indirectly accounts for the depreciation cost as well as ageing)

1.3 Estimated Age of the machine (if retrofitting/reconditioning/up-gradation is done)- accounts for how long the investment on retrofitting can provide the productivity)

1.4 Age of the new machine (in case of machine retirement ) – Account for how long investment on the procurement of new machine can provide productivity

2. Parameters that count for technology and productivity factors 2.1 Is Control system of the machine under consideration is manufactured by OEM? 2.2 Is the spares fitted on the machine that are proprietary in nature are provided by the

OEM? (these above two parameters accounts for the technological obsolescence of the machine)

2.3 Availability of the machine (Accounts for the efficiency, effectiveness and productivity of the machine, this factor is primarily depending on the MTTR, MTBF, OEE, % of breakdown time)

2.4 Mechanical Condition of the Machine (Accounts for the Accuracy of the machine under consideration, this factor is primarily dependent upon the Geometrical Accuracy Test and Laser Positioning Accuracy test as per widely used International standards only)

2.5 Substantial Change in the production Technology (Account for the case where manufacturing cycle of a job can be substantially reduced and hence productivity can be increased using new production technology)

It should be clear that 2.5 does not count for the technological obsolescence, here technological obsolescence is considered to be the obsoleteness in the control system which is designed for a particular production technology, so there may be the case that new control system is following the same production technology as the obsolete one was following.



After deciding the responsible parameters the next step is to choose the suitable problem solving approach. The choice will be from Classical problem solving approach and Artificial Neural Network problem solving approach. Among the conclusions of the extensive review of neural network literature by Zhang et al (1998) that a considerable amount of research has been done in this area. The findings are inconclusive as to whether and when Artificial Neural Networks are better than classical methods. In this paper I choose the later problem solving technique i.e. Artificial Neural Network Problem Solving Approach

In the Models studied in this paper, Input Layer contains 9 neurons and output layer contains 1neuron which indicates the performance index of the retrofitting/reconditioning/upgradation. Let ‘P’ be the performance index

1 0 (12)

Output of the ith neuron of the hidden layer h1 is given by the equation

∑ . (13)

Similarly output of the kth neuron of the hidden layer h2 (if used) is given by the equation

∑ . (14)

Output Layer Neuron is driven by the equation

∑ . ) (15)

Where - denotes the weighted connection between the input layer i to jth neuron.

nh1 – Number of neurons in hidden layer h1. nh2 – Number of neurons in hidden layer h2.

The decision of nh1, nh2 is done on hit n trial basis, some random nh1, nh2 is selected and training performance is calculated, best on the best performance nh1,nh2 selected. ‘trainlm’ is used for the training method in this neural network. Input neurons of the neural network 1. Cost of Similar type of new Machine (in lacs) (x1) 2. Age of the machine under consideration (in years) (x2) 3. Estimated age of the Machine after retrofitting/Reconditioning/Upgradation done (typically 2-

10 years) (x3) 4. Age of the New Machine if procured (in years) (x4) 5. Availability of the machine (based on MTTR,MTBF,OEE,% breakdown in specified time)

(x5) 6. Control system is presently manufactured by OEM or Not. (x6) 7. Spares of the Control system and other Parts are provided by OEM or not. (x7) 8. Mechanical condition of the machine (determined by Geometrical Accuracy tests and Laser

positioning Accuracy tests. (x8) 9. Substantial Change in the production technology. (x9) 10. Retrofitting Cost of the Machine under consideration (x10) (in lacs)

Factors x1-x4 shown above can be directly obtained from the machine database, for other parameters following methodology is used



Based on the values of the MTTR (Mean Time To Repair), MTBF (Mean Time Between Failure), OEE (Overall Equipment Effectiveness), % resolution of breakdown, CM (Cost of Maintenance), the factor x5 can be defined as

,

, (

16) Where subscript ‘T’ denotes the threshold values of these parameters which are decided by the maintenance and production department on annually basis.

1,

1, (17)

1,

1, (18)

1,

1, (19)

Where 1‐Geometrical Accuracy Tests 2‐ Laser Positional Accuracy Test

1,

1, (20)

Where is the expected job cycle time on new technology, is the Job cycle time on existing technology, is the minimum threshold improvement ratio, typically it value should be greater than 1.2. , , , , , , , (21)

At the timing of training the network values of x1- x10 are given from the data, and at the time of Prediction of Retrofitting/Reconditioning/Up-gradation cost, we change the value of x10 from 1 to x1 (As the retrofitting cost cannot be greater than the cost of similar type of new machine) and calculates the value of ‘P’ for each value of x10. Let be the maximum investment that can be done for the Retrofitting/Reconditioning/Up-gradation of the machine then

max 1 (22)



3.5 Algorithm/MATLAB Script

sprintf('%s','Machine Replacement Model v1.0') % label a clear; ttmode=input('Enter the Mode\n 1.Training the Neural Network 2.Use the network :'); if(ttmode == 1), training_input=xlsread('ipv4.xlsx'); training_output=xlsread('opv4.xlsx'); nhl=input('Enter the number of hidden layer 1/2: '); if(nhl==1), nhn=input('Enter the number of hidden neurons for your network : '); act1=input('Enter the activation function [purelin/logsig/tansig] : ','s'); net=newff(training_input,training_output,nhn,{act1}); else nhn1=input('Enter number of hidden neuron in first layer : '); nhn2=input('Enter number of hidden neuron in second layer : '); act2=input('Enter the activation function for layer 1 [purelin/logsig/tansig]: ','s'); act3=input('Enter the activation function for layer 2[purelin/logsig/tansig]: ','s'); net=newff(training_input,training_output,{nhn1,nhn2},{act2,act3}); end net.trainParam.max_fail=6; [net,tr]=train(net,training_input,training_output); h2=plotperf(tr); %title('Training of Neural Network \\n Machine Replacement Model'); saveoption=input('Do you want to save the network Y/N : ', 's'); if(saveoption=='y') nname=input('Enter the name of the network : ','s'); ext1='.mat'; savefilename=strcat(nname,ext1); save(savefilename); end clear; elseif(ttmode == 2) netnamel=input('Enter the name of network u want to load : ','s'); ext='.mat'; loadfilename=strcat(netnamel,ext); load(loadfilename); name=input('Enter the name of the machine under consideration : ','s'); nc=input('Enter the cost of similar type of new machine(in lakhs): '); ar=input('Enter the Age of Macihne under consideration after retrofitting(in years): '); an=input('Enter the Age of similar type of new machine(in years): '); ac=input('Enter the current Age of the machine under consideration(in years) : '); av=input('Enter the Availability Index of the machine under consideraion : '); cs=input('Enter control system is presently produced by OEM 1:yes -1:No : '); s=input('Enter weather spares are provided 1:yes -1:No : '); m=input('Enter Mechanical condition of the machine 1:OK -1:Not OK : '); sp=input('Substantial Change in production technology 1:Yes -1:No : '); rc=0; for i=1:1000 rc=rc+nc/1000; r(i)=rc; input_vector=[rc;nc;ar;an;ac;av;cs;s;m;sp]; result=sim(net,input_vector); if(result>=0.99) c=rc; end



o(i)=result; end h=plot(r,o); xlabel('Retroffiting Costs in Lacs'); ylabel('Performance index of Retroffiting'); s1='Machine Replacement Model Using Neural Network'; s2='Machine under study : '; s3=name; s4=strcat(s2,s3); s8=['Cost of similar type of New Machine(in lacs) : ' num2str(nc)]; s9=['Age of Macihne under consideration after retrofitting(in years) : ' num2str(ar)]; s10=['Age of similar type of new machine(in years) : ' num2str(an)]; s11=['current Age of the machine under consideration(in years) : ' num2str(ac)]; s12=['Availability Index of the machine under consideraion : ' num2str(av)]; s13=['Control system is presently produced by OEM : ' num2str(cs)]; s14=['spares are provided : ' num2str(s)]; s15=['Mechanical condition of the machine : ' num2str(m)]; s16=['Substantial Change in production technology : ' num2str(sp)]; s20=[‘Maximum Investment that can be done (in lacs) : ‘ numstr(c)]; s5=char(s1,s4,s8,s9,s10,s11,s12,s13,s14,s15,s16); s6='.pdf'; s17='.bmp'; s7=strcat(s3,s6); s18=strcat(s3,s17); title({s1;s4;s8;s9;s10;s11;s12;s13;s14;s15;s16;s20},'HorizontalAlignment','center'); filesaveoption=input('Do you want to save the figure report (Y/N) : ','s'); if(filesaveoption == 'y') saveas(h,s7); saveas(h,s18); end else sprintf('%s','Error Press 1/2 only') end



4. Prediction Performance In table-1 I present the summary of prediction performance statistics for the cost of retrofitting/reconditioning/upgradation. Based on the MSE, the best neural network is selected, it is observed that MSE for training and validation comes out to be very satisfactorily. I found that best neural network model fails in 1/8238 samples provided to it. Performance plot of Training, Validation and testing generated by MATLAB is shown in fig-6. The best validation performance is calculated as 3.86 . Fig 6A shows the confusion matrix for the network 100% in the blue area indicates the perfect training of the network. Fig 6B Shows the Neural network Feed forward architecture for the best network. All the figures are generated by MATLAB (The MATHWORKS 2010 R2010a, Neural Network Toolbox 6.0)

Neural Network Name

Hidden Layers

No. of neurons in Layer

1

No. of neurons in Layer

2

Activation

Function of layer1

Activation Function of layer2

Mean Square

Error (MSE) (Validation)

Gradient Performance

(MSE of Training)

neth1nh12tansig

1 2 ‐ tansig ‐ 0.002679 at epoch

50 2.75E‐06 0.00132

neth1nh13tansig


21 1.49E‐05 0.000196

neth1nh14tansig

1 4 ‐ tansig ‐ 0.00245 at epoch 19

2.75E‐06 0.00289

neth1nh15tansig

1 5 ‐ tansig ‐ 0.0022 at epoch 20

8.90E‐08 0.00156

neth1nh16tansig


36 5.58E‐05 0.000117

neth1nh17tansig

1 7 ‐ tansig ‐ 0.00111 at epoch 16

9.68E‐09 6.88E‐06

neth1nh18tansig

1 8 ‐ tansig ‐ 6.4 e‐4 at epoch 49

0.00133 2.36E‐04

neth1nh19tansig

1 9 ‐ tansig ‐ 1.24 e‐4 at epoch 38

1.09E‐04 2.22E‐05

neth1nh110tansig

1 10 ‐ tansig ‐ 0.0010846 at epoch

33 4.68E‐05 1.02E‐05

neth1nh111tansig

1 11 ‐ tansig ‐ 7.98 e‐5 at epoch 26

2.57E‐05 0.000135

neth1nh112tansig

1 12 ‐ tansig ‐ 9.23 e‐4 at epoch 37

8.67E‐05 2.56E‐04

neth1nh113tansig

1 13 ‐ tansig ‐ 9.43e‐4 at epoch 27

7.16E‐05 9.77E‐05

neth1nh114tansig

1 14 ‐ tansig ‐ 0.000249 at epoch

19 0.00242 0.00249

neth1nh115tansig

1 15 ‐ tansig ‐ 0.000983 at epoch

12 1.89E‐05 0.000126

neth1nh116tansig

1 16 ‐ tansig ‐ 0.000732 at epoch

19 2.06E‐05 2.93E‐05

neth1nh117tansig

1 17 ‐ tansig ‐ 2.35 10‐4 at epoch

25 5.49 10‐4 7.39E‐05



neth1nh118tansig

1 18 ‐ tansig ‐ 0.00121 at epoch 8

0.00127 3.94E‐06

neth1nh119tansig

1 19 ‐ tansig ‐ 4.8 10‐4 at epoch 37

0.00089 0.00026

neth1nh120tansig

1 20 ‐ tansig ‐ 1.275 10‐4 at epoch

36 0.0184 0.000151

neth2nh14nh22purelintansig

2 4 2 purelin tansig 0.0044 at epoch 28

1.45E‐06 0.00373



0.00135 0.00233


2 10 4 purelin tansig 5.4 10‐4 at epoch 13

1.50E‐06 0.000209



5.90E‐09 3.2 10‐3


2 8 4 purelin tansig 1.59e‐14 at epoch 57

9.00E‐11 2.23E‐17


2 12 4 purelin tansig 9.26e‐5 epoch 18

1.73E‐08 1.44E‐07



0.0001 0.00348



0.0001 0.003



0.00216 0.00034



8.00E‐05 0.000205



1.00E‐05 0.00335


2 20 5 purelin tansig 3.86e‐5 at epoch 20

5.23E‐05 0.000214



0.00139 0.00259

Table 1: Performance of different networks (Best network is marked with Bold and different colour)



Fig 6 : Performance Plot of Best Neural Network for the prediction of Retrofitting /Reconditioning/Upgradation of CNC Machine

Fig 6A : Confusion Matrix for the Network (100% shows perfect training)



Fig 6B : Neural Network Architecture for the best Network

In order to test the neural network, the neural network is simulated by providing training input from the data samples and outputs generated by neural network are recorded as simulated outputs. Fig 7 shows the relationship between training outputs from the data and simulated outputs generated by neural network. Y=X type of graph shows the perfect training of the neural network.



Fig 7 : Plot ‘Desired Outputs’ Vs ‘Trained Outputs for the best network (Linear Relationship shows that the neural network is correctly

trained)

Fig 8 shows the relationship of error (training output – simulated output) Vs simulated outputs. The maximum error recorded is close to 10 which is exceptionally good. Fig 10 shows how the training of neural network proceed with respect to epochs. The training lasts for 57 epochs and stops due to continuous validation fail.

Fig 8 : Error Vs Output for Best Network (Max Error≈10^-6)

-0.2 0 0.2 0.4 0.6 0.8 1 1.2-2.5

-2

-1.5

-1

-0.5

0

0.5

1x 10

-6

Output of Neural Network

Err

or in

neu

ral n

etw

ork

(tra

inin

g ou

tput

-Act

ual o

utpu

t)



Fig 9 : 3-D plot of ‘Desired Outputs’ , ‘Trained Outputs’, ‘Training Inputs’ for the best network

Fig 10 : MSE Vs Epoch for best network

Fig 11, 13, 15 shows the weight connections between the neurons of input layer and hidden layer1, hidden layer1 and hidden layer2, hidden layer2 and output layer respectively, Fig 12,14 shows the contour plot for the weight connection from input layer to hidden layer h1 and from hidden layer h1 to hidden layer h2 respectively while contour map for the hidden layer h2 and output layer is not possible as weight matrix is too small, while fig 16 shows the bias weights of the neuron in the different layers.



Fig 11: Weight Connections 1

Fig 12: Contour Map for Weight Connection between Input Layer and hidden layer h1

1 2 3 4 5 6 7 8-15

-10

-5

0

5

10

Rows of the Weight Matrix (From input layers to first hidden layer)

Wei

ghts

(ea

ch d

ot s

how

wei

ght

for

part

icul

ar c

olum

n)Weight connections between Input Layer and first hidden layer



Fig 13: weight connections 2

Fig 14: Contour Map for Weight Connection between hidden layer h1 and hidden layer h2

1 1.5 2 2.5 3 3.5 4-15

-10

-5

0

5

10

15

Rows of weight matrix

Wei

ghts

(ea

ch d

ot s

how

the

wei

ght

for

a pa

rtic

ular

col

umn)

Weight connections between first layer and second layer

-7.61

65-5.5

742 -5

.5742

-5.5

742

-3.5319

-3.53

19

-3.5319

-3.5319

-3.53

19

-3.5319

-1.4895

-1.4895

-1.4

895

-1.4895

-1.4895

-1.48

95

-1.48

95

-1.4895

0.55

276

0.55276

0.55276

0.55

276

0.55276

0.55

276

0.552762.5951

2.5951

2.5951

2.5951

4.63

744.637

4

4.6374

6.6797

6.6797

8.722

Contour Map for the Weight Connections between hidden layer h1 and hidden layer h2

1 2 3 4 5 6 7 81

1.5

2

2.5

3

3.5

4



Fig15: weight connection 3

Fig 16 : Bias weights for neurons in Neural Network

Fig 17 shows the regression analysis of the network, the value obtained are m=1, b=1.2 , r=1 which shows the perfect fit of the data samples

1 1.5 2 2.5 3 3.5 4-1.5

-1

-0.5

0

0.5

1

1.5

Rows of wieght matrix

Wei

ghts

Weight Connection between second hidden layer and the output layer

1 2 3 4 5 6 7 8-3

-2

-1

0

1

2

3

Neurons

Bia

s W

iegh

ts

Bias Weight Connections in Neural Network

Bias Weights for Hidden Layer 1

Bias Weights for Hidden Layer 2Bias Weight for Output Layer



Fig 17 : Regression Analysis of the network (m=1, b=1.2e-12)

4.1 Few Predictions made by the best network

Fig 18 shows the sample report of prediction created by the algorithm discussed in section 3. It determines the value of Cmax that can be invested on the basis of given parameters. Table 2 shows some abstract data sets formed and neural network is tested on these datasets and value of Cmax is determined for each datasets. Fig 19 shows the plot between performance index and retrofitting cost for each data set.

Fig 18: Prediction made by the best network on the given set of inputs

0 100 200 300 400 500 600 700 800 900 1000-0.2

0

0.2

0.4

0.6

0.8

1

1.2 X: 344Y: 0.9907

Retroffiting Costs in Lacs

Per

form

ance

inde

x of

Ret

roff

iting

Machine Replacement Model Using Neural NetworkMachine under study :1

Cost of similar type of New Machine(in lacs) : 1000Age of Macihne under consideration after retrofitting(in years) : 8

Age of similar type of new machine(in years) : 20current Age of the machine under consideration(in years) : 20

Availability Index of the machine under consideraion : -1Control system is presently produced by OEM : -1

spares are provided : -1Mechanical condition of the machine : 1

Substantial Change in production technology : -1Maximum Investment that can be done(in lacs) : 344

X: 374Y: 0.003629



Fig 19 : Performance Index Vs Cost for the different data set as depicted in table-2

Parameters Data Set-1

Data Set-2

Data Set-3

Data Set-4

Data Set-5

Data set-6

Data Set-7

Data Set-8

Data Set-9

Data Set-10

X1 1000 1000 500 1000 1000 1000 1000 1000 1000 1000 X2 8 5 8 8 8 8 8 8 8 8 X3 20 20 20 20 20 20 20 20 20 10 X4 20 20 20 40 20 5 20 20 20 20 X5 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 X6 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 X7 -1 -1 -1 -1 -1 1 -1 -1 1 -1 X8 1 1 1 1 -1 1 -1 -1 1 1 X9 -1 -1 -1 -1 -1 -1 1 1 -1 -1

Cmax (in lacs)

344 229 178 305 637 NS* 287 763 342 589

Table 2 : Prediction made by Best Network for the given data sets (Max value that can be invested is shown by Cmax value)

*-activity selected is Not Suitable 5. Conclusion

This paper seeks to determine whether accurate prediction of cost of Retrofitting/Reconditioning/Up-gradation of CNC Machines can be developed using neural network. I found that the best neural network produces a Validation MSE of 3.861 , Training MSE , Test MSE . With the reliable prediction of cost, decision maker can therefore more accurately decide the Retrofitting projects and their costing. The Retrofitting cost is calculated for the abstract data (see table 2). From Table 2 it is clear that if the mechanical condition of the machine is not ok and the age of the machine is greater than 15 years then high cost of retrofitting of the CNC machine under consideration is justified. If the machine is new i.e. age of the machine is less than 5 years and Availability of the Machine is less than the expected then also going for the retrofitting is not suitable, if the cost is greater than 10% of the machine’s cost. Moreover the cost shown in the table-2 indicates the maximum retrofitting cost that can be invested on the machine. The increased accuracy of the prediction is likely to originate from the ability of neural network to capture non-linear relationships. Although the considerable MSE is observed in the trained neural network but different training algorithms may be chosen like traingda, traingdx, trainrp, reduced memory trainlm etc and performance in each can be

0 100 200 300 400 500 600 700 800 900 1000-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Retrofitting/Reconditioning/Upgradation cost (in lacs)

Per

form

ance

Ind

ex o

f th

e A

ctiv

ity

data set-1data set-2

data set-3

data set-4


data set-7

data set-8




compared and best can be chosen. Although the results are particularly based on the data for CNC machines, but it will be interesting to check the model for the Non-CNC Machines, Robotics Machines, other special purpose machines and process plants used in Automobile sectors, power sectors, Sugar Industries etc. In this paper feed forward network is used for the modelling but it is interesting to use the data samples to train the recurrent networks, or particularly the pattern recognition networks. In this paper only deterministic activation functions (tansig, logsig, purelin) are used, it will be interesting to use the non-deterministic activation function of the output layer.

APPENDIX-A Data

The Data is collected from the various manufacturing industries in India including Power Equipment Manufaturing Industries, Sugar Industries, Automobiles Industries. Data Compiled for more than 700 CNC Machines, out of which more than 300 CNC upgradation/retrofitting/reconditioning projects are completed and the data of these projects is the basis of training samples to the neural network. Following are the few Additional Assumptions taken in order to create Additional data sets.

i. If the Retrofitting cost is greater than the cost of new machine, then irrespective of other parameters, Retrofitting is not suitable.

ii. If the machine under consideration is very new (procured within 5 years) , any retrofitting cost greater than 10% of the cost of the machine is not advisable, as depreciation of the machine can be assumed to be 10%.

iii. If the estimated age of machine after retrofitting is very less (less than 3 years) then retrofitting is not advisable, irrespective of other parameters.

References

[1] Howard Demuth, Mark Beale, Martin Hagan (2007). MATLAB Neural Network Toolbox 5 User Guide, 5.12-5.73. [2] Simon Haykin (2005). Neural Networks-A Comprehensive Foundation, 183-248 [3] Cesare Alippi (2002). IEEE Transactions on circuits and systems-I:Fundamental Theory and Applications, Vol 49, No. 12., 1799-1809 [4] Poli I, R.D.Jones (1994). A neural net model for Prediction. Journal of American Statistical Association 89, 117-121 [5] James A. Freeman,(1991). Neural Network Algorithms, Applications, Programming Techniques, 89-124 [6] Michael A Arbib (2002). The Handbook of Brain theory and neural networks 2nd Edition, MIT Press, 144-147 [7] Martin S. Feldstein, Michael Rothschild (1974), Towards an Economic Theory of Replacement Investment, Econometrica, Vol 42,

393-403.



neural network for the prediction of retrofitting ......cnc system refers to the automation of...

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