Tugas Pemodelan - Model Regresi Polinomial

7/25/2019 Tugas Pemodelan - Model Regresi Polinomial

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Afham Ramadhan Kuliah Pemodelan dan Rekayasa Sistem

S2 Teknik Elektro

Tugas pemodelan

Membuat model regresi polinomial dari data berikut

No. Solids reduction x (%) Chemical oxygen demand, y (%)

1 3 5

2 7 11

3 11 21

4 15 16

5 18 16

6 27 28

7 29 27

8 30 25

9 30 35

10 31 30

11 31 40

12 32 32

13 33 34

14 33 32

15 34 34

16 36 37

17 36 38

18 36 34

19 37 36

20 38 38

21 39 37

22 39 36

23 39 45

24 40 39

25 41 41

26 42 40

27 42 44

28 43 37

29 44 44

30 45 46

31 46 4632 47 49

33 50 51


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S2 Teknik Elektro

Membuat model dari persamaan polinomial dengan metode Least Square

Input : x

[

]


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S2 Teknik Elektro

Polinomial orde satu

H =

[ 1 3 ]

1 7

1 111 15

1 18

1 27

1 29

1 30

1 30

1 31

1 31

1 32

1 33

1 33

1 34

1 36

1 36

1 36

1 37

1 38

1 39

1 39

1 39

1 40

1 41

1 421 42

1 43

1 44

1 45

1 46

1 47

1 50

....


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S2 Teknik Elektro [ 6.5406 ]

10.1551

13.7697

17.3843

20.0952

28.2280

30.0353

30.9389

30.9389

31.8426

31.8426

32.7462

33.6499

33.6499

34.5535

36.3608

36.360836.3608

37.2644

38.1681

39.0717

39.0717

39.0717

39.9754

40.8790

41.7826

41.7826

42.686343.5899

44.4936

45.3972

46.3009

49.0118

Akumulasi kuadrat error : .

Persamaan Polinomial orde empat :

y = -7E-06x4+ 0.0009x

3- 0.0407x

2+ 1.5074x + 2.0835

persamaan polinomial orde dua :

=

[1.5406]

-0.8449

-7.2303

1.3843

4.0952

0.2280

3.0353

5.9389

-4.0611

1.8426

-8.1574

0.7462

-0.3501

1.6499

0.5535-0.6392

-1.6392

2.3608

1.2644

0.1681

2.0717

3.0717

-5.9283

0.9754

-0.1210

1.7826

-2.2174

5.6863

-0.4101

-1.5064

-0.6028

-2.6991

-1.9882


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S2 Teknik Elektro H =[ 1 3 9 ]

1 7 49

1 11 121

1 15 2251 18 324

1 27 729

1 29 841

1 30 900

1 30 900

1 31 961

1 31 961

1 32 1024

1 33 1089

1 33 1089

1 34 11561 36 1296

1 36 1296

1 36 1296

1 37 1369

1 38 1444

1 39 1521

1 39 1521

1 39 1521

1 40 1600

1 41 1681

1 42 1764

1 42 1764

1 43 1849

1 44 1936

1 45 2025

1 46 2116

1 47 2209

1 50 2500

...

.. .Persamaan polinomial orde dua :

y = 0.0028x2+ 0.7504x + 5.4281


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S2 Teknik Elektro

[ 7.7047]

10.8196

14.0252

17.321519.8532

27.7546

29.5728

30.4904

30.4904

31.4137

31.4137

32.3426

33.2772

33.2772

34.217536.1151

36.1151

36.1151

37.0724

38.0354

39.0040

39.0040

39.0040

39.9783

40.9583

41.9439

41.9439

42.9352

43.9322

44.9349

45.9432

46.9572

50.0332

=

[ 2.7047 ]

-0.1804

-6.9748

1.3215

3.8532

-0.2454

2.5728

5.4904

-4.5096

1.4137

-8.5863

0.3426-0.7228

1.2772

0.2175

-0.8849

-1.8849

2.1151

1.0724

0.0354

2.0040

3.0040

-5.99600.9783

-0.0417

1.9439

-2.0561

5.9352

-0.0678

-1.0651

-0.0568

-2.0428

-0.9668

.

Akumulasi kuadrat error :

Error rata-rata :

9.6117


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S2 Teknik Elektro

Persamaan Polinom orde tiga : H = [ 1 3 9 27 ]

1 7 49 343

1 11 121 1331

1 15 225 3375

1 18 324 5832

1 27 729 19683

1 29 841 24389

1 30 900 27000

1 30 900 27000

1 31 961 29791

1 31 961 29791

1 32 1024 32768

1 33 1089 35937

1 33 1089 359371 34 1156 39304

1 36 1296 46656

1 36 1296 46656

1 36 1296 46656

1 37 1369 50653

1 38 1444 54872

1 39 1521 59319

1 39 1521 59319

1 39 1521 59319

1 40 1600 64000

1 41 1681 68921

1 42 1764 74088

1 42 1764 74088

1 43 1849 79507

1 44 1936 85184

1 45 2025 91125

1 46 2116 97336

1 47 2209 103823

1 50 2500 125000

.... .. . .

Persamaan Polinomial orde tiga :

y = 0.0002x3- 0.0153x

2+ 1.1741x + 3.2189


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S2 Teknik Elektro

[ 6.6097 ]

10.7640

14.5763

18.1303

20.6768

28.0817

29.7467

30.5897

30.5897

31.4414

31.4414

32.3033

33.1765

33.176534.0624

35.8775

35.8775

35.8775

36.8094

37.7592

38.7282

38.7282

38.7282

39.7178

40.729241.7638

41.7638

42.8229

43.9078

45.0198

46.1602

47.3304

51.0322

=

[ 1.6097 ]

-0.2360

-6.4237

2.1303

4.6768

0.0817

2.7467

5.5897

-4.4103

1.4414

-8.5586

0.3033

-0.8235

1.17650.0624

-1.1225

-2.1225

1.8775

0.8094

-0.2408

1.7282

2.7282

-6.2718

0.7178

-0.27081.7638

-2.2362

5.8229

-0.0922

-0.9802

0.1602

-1.6696

0.0322

.Akumulasi kuadrat error :Error rata-rata :

9.4609


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S2 Teknik Elektro

Dengan cara yang sama maka untuk mencari nilai error terkecil polinomial berikut adalah :

Orde empat :

Orde lima :

[4]

[.....]

.

.. . . .4y = -7E-06x

4+ 0.0009x

3- 0.0407x

2+ 1.5074x + 2.0835


Error rata-rata :

9.4354

[

45] [

...... ]

... . . .4 .5y = 4E-06x

5- 0.0005x

4+ 0.0249x

3- 0.5597x

2+ 6.0305x - 8.9618


Error rata-rata :

8.6126


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S2 Teknik Elektro

orde enam :

GRAFIK

0 5 10 15 20 25 30 35 40 45 505

10

15

20

25

30

35

40

45

50

55

y = 0.9*x + 3.8

data1

linear

[

456]

[....... ]

.

.. . . .4 .5 .6y = -1E-07x

6+ 2E-05x

5- 0.0018x

4+ 0.0656x

3- 1.1678x

2+ 10.017x - 16.964


Error rata-rata :

8.405


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S2 Teknik Elektro

0 5 10 15 20 25 30 35 40 45 505

10

15

20

25

30

35

40

45

50

55

y = 0.0028*x2+ 0.75*x + 5.4

data1

quadratic

0 5 10 15 20 25 30 35 40 45 505

10

15

20

25

30

35

40

45

50

55

y = 0.00022*x3- 0.015*x2+ 1.2*x + 3.2

data1

cubic


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S2 Teknik Elektro

0 5 10 15 20 25 30 35 40 45 505

10

15

20

25

30

35

40

45

50

55

y = - 6.6e-06*x4+ 0.00093*x3- 0.041*x2+ 1.5*x + 2.1

data1

4th degree

0 5 10 15 20 25 30 35 40 45 505

10

15

20

25

30

35

40

45

50

55

y = 3.5e-06*x

5

- 0.00049*x

4

+ 0.025*x

3

- 0.56*x

2

+ 6*x - 9

data1

5th degree


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S2 Teknik Elektro

0 5 10 15 20 25 30 35 40 45 505

10

15

20

25

30

35

40

45

50

55

y = - 1.3e-07*x

6

+ 2.5e-05*x

5

- 0.0018*x

4

+ 0.066*x

3

- 1.2*x

2

+ 10*x - 17

data1

6th degree

0 5 10 15 20 25 30 35 40 45 505

10

15

20

25

30

35

40

45

50

55

y = - 2.6e-08*x7

+ 4.7e-06*x6

- 0.00035*x5

+ 0.013*x4

- 0.24*x3

+ 2.2*x2- 7.1*x + 12

data1

7th degree


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S2 Teknik Elektro

0 5 10 15 20 25 30 35 40 45 505

10

15

20

25

30

35

40

45

50

55

y = 1.5e-09*x8- 3.6e-07*x7+ 3.5e-05*x6- 0.0018*x5+ 0.054*x4-

0.91*x3+ 8.2*x2- 33*x + 51

data1

8th degree

0 5 10 15 20 25 30 35 40 45 505

10

15

20

25

30

35

40

45

50

55

y = - 1.8e-10*x

9

+ 4.6e-08*x

8

- 5e-06*x

7

+ 0.0003*x

6

- 0.011*x

5

+ 0.25*x4- 3.4*x3+ 26*x2- 1e+02*x + 1.4e+02

data1

9th degree

Tugas Pemodelan - Model Regresi Polinomial

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