1.0 INTRODUCTION

2.0 DATA SET

Input data

Box width(m) = w

Box height(m) = h

Fill height(m) = H

Reinforcement provided (mm2) = A

Output data

Thickness of box (mm) = t

Our organization Road Development Authority design structures for roads .Box culverts are

the main type of drainage structures we designed,In our organization we have typical culvert

table for different sizes and different fill height ,That can be use to train a neural network for

predicting unknown parameters

Total number of data = 37

2/3 Number of data = 25

Number of training examples = 25

Number of testing examples = 12

w(m) h(m)

fill height

H(m)

RF Area A

(mm2/m)

1005

top slab

thickness t

(mm)

200

2 2 1 0 1795 250

1 1 1 0

Data set

3 1 1.5 0 1005 225

4 1.5 1.5 0 1340 200

5 2.5 1.5 0 2094 225

6 1 2 0 1005 200

7 2 2 0 1795 225

8 2.5 2 0 2094 225

9 1.5 2.5 0 1340 200

10 2 2.5 0 1795 225

11 3 1 0 1608 275

12 3 1.5 0 1608 275

13 3 2 0 1340 275

14 3.5 1 0 1608 300

15 3.5 1.5 0 1608 300

16 3.5 2.5 0 2094 350

17 4 1 0 2094 350

Training

17 4 1 0 2094 350

18 4 1.5 0 2094 350

19 4 2.5 0 2094 350

20 2 2 2 1340 250

21 2 2 4 1795 300

22 3 2 2 1340 300

23 3 2 6 2094 400

24 3 3 2 1340 300

25 3 3 6 2094 400

1 1.5 1 0 1340 200

2 2.5 1 0 2094 225

3 2 1.5 0 1795 225

4 1.5 2 0 1340 200

5 1 2.5 0 1005 200

6 2.5 2.5 0 2094 225

7 3 2.5 0 1340 275

8 3.5 2 0 2094 300

9 4 2 0 2094 350

12 3 3 4 1795 350

10 2 2 6 2094 350

11 3 2 4 1795 350

Testing

3.0 NURAL NETWORK

WinNN32 software used to train and test data set

3.1 TRAIN 4:3:1 NURAL NETWORK

Input layer nodes Mid layer nodes Output layer node

The raw data was normalized before training to get better performance. Eta and Alpha values

were set to 0.5. Sigmoid transfer function used and target error values adjusted so that 90%

or more good patterns achieve. Here three and two middle layers were tried with two

different target errors. This had given four distinct predictions.

Same data set is used in mathematical regression and test data set was tested accordingly.

All out put data with Mean absolute error and 1-Ratioaverage is displayed

Number of parameters = 4 x 3 + 3 + 3 x 1 + 1 = 19

No of parameters x 1.5 = 19 x 1.5

= 28.5

Number of training examples = 25

But it is possible to train above neural network since number of parameter are less than the

training example available

Artificial Neural Network (3 middle nodes and target error of 0.01)prediction slab

thickness(mm)

225

219 225

212 200

216 200

255 225

1.08

351 350

329 350

Network Target

Mean

Absolute

error

16

30

6

12

13

16

8

25

1

21

I 1-RAVG I

1.13

0.97

1.06

1.06

1.07

1.03

1.08

1.00

0.94

283 275

325 300

213 200

241

376 350 26

14364 350

16

1.07

1.04

0.05

Artificial Neural Network (3 middle nodes and target error of 0.005)prediction slab

thickness(mm)

Network Target

Mean

Absolute

error

I 1-RAVG I

229 200 29 1.14

229 225 4 1.02

220 225 5 0.98

205 200 5 1.03

202 200 2 1.01

228 225 3 1.01

283 275 8 1.03

337 300 37 1.12

352 350 2 1.00

365 350 15 1.04

392 350 42 1.12

391 350 41 1.12

16 0.05

3.2 TRAIN 4:2:1 NURAL NETWORK

Input layer nodes Mid layer nodes Output layer node

Number of parameters = 4 x 2 + 2 + 2 x 1 + 1 = 13Number of parameters = 4 x 2 + 2 + 2 x 1 + 1 = 13

No of parameters x 1.5 = 13 x 1.5

= 19.5

Number of training examples = 25

Artificial Neural Network (2 middle nodes and target error of 0.01)prediction slab

thickness(mm)

Network Target

Mean

Absolute

error

I 1-RAVG I

222 200 22 1.11

248 225 23 1.10

224 225 1 0.99

217 200 17 1.08

215 200 15 1.08

238 225 13 1.06

277 275 2 1.01

331 300 31 1.10

343 350 7 0.98

314 350 36 0.90

379 350 29 1.08379 350 29 1.08

379 350 29 1.08

19 0.05

Artificial Neural Network (2 middle nodes and target error of 0.005)prediction slab

thickness(mm)

Network Target

Mean

Absolute

error

I 1-RAVG I

211 200 11 1.05

233 225 8 1.03

219 225 6 0.97

212 200 12 1.06

209 200 9 1.05

247 225 22 1.10

282 275 7 1.02

325 300 25 1.08

354 350 4 1.01

399 350 49 1.14

332 350 18 0.95332 350 18 0.95

318 350 32 0.91

17 0.03

4.0 MULTIPLE REGRESSION ANALYSIS

from above analysis we can write slab thickness as

slab thickness t = 138.7 + 49.774w -2.719h + 18.032H - 0.00000796A

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.949

R Square 0.901

Adjusted R Square 0.881

Standard Error 21.471

Observations 25

ANOVA

df SS MS F Significance F

Regression 4 83680 20920 45 9.27818E-10

Residual 20 9220 461

Total 24 92900

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 138.732 23.581 5.883 0.000 89.542 187.922

w 49.774 6.197 8.032 0.000 36.848 62.700

h -2.719 8.001 -0.340 0.738 -19.409 13.971

H 18.032 2.712 6.650 0.000 12.376 23.688

A -0.00000796 0.016 -0.001 1.000 -0.033 0.033

slab thickness t = 138.7 + 49.774w -2.719h + 18.032H - 0.00000796A

355 350 5 1.01

352 350 2 1.01

13 0.03

307 300 7 1.02

332 350 18 0.95

341 350 9 0.97

182 200 18 0.91

256 225 31 1.14

281 275 6 1.02

260 225 35 1.16

234 225 9 1.04

208 200 8 1.04

Network Target

Mean

Absolute

error

I 1-RAVG I

211 200 11 1.05

5.0 RESULTS COMPARISON FOR DIFFERENT MODELS

6.0 DISCUSSION

Results of four Artificial Neural Networks and Multiple regressions are summarized in above

table . Both mean absolute error and 1- ratio average zero are desired

From results of Artificial Neural Networks minimum mean absolute error of 16mm observed

from three middle layer node . This may due to lager number of links tend to fit more with the

trained data examples. Also lager target error avoids sub local maximums and minims.

3 Middle layer nodes 2 Middle layer nodesMultiple

Regression

16

0.05

16 19 17 13

0.05 0.05 0.03 0.03

Mean

Absolute

error

I 1-RAVG I

Error = 0.01 Error = 0.005 Error = 0.01 Error = 0.005

When comparing Artificial Neural Networks and Multiple Regression results, lowest mean

absolute error was given by Multiple Regression method. This may due to lack of training

examples of Artificial Neural Networks. But generally ANN should give better results than MR.

ANNEXURES

WinNN32 software interface for 4 2 1 model of error 0.01

WinNN32 software interface for 4 2 1 model of error 0.005

WinNN32 software interface for 4 3 1 model of error 0.01

WinNN32 software interface for 4 3 1 model of error 0.005