Laporan Pemodelan Dan Simulasi

LAPORAN TUGAS BESAR PEMODELAN DAN SIMULASI Diajukan untuk memenuhi salah satu tugas mata kuliah Pemodelan dan Simulasi Dosen Gani Gunawan, S.T., M.T. Disusun oleh : 10107206

Sarah R Puri

10108286

Juli Rizki A

10108279

Irwansyah

10107349

Guruh Wiraajiputro

10107636

Elan Maulana

JURUSAN TEKNIK INFORMATIKA FAKULTAS TEKNIK DAN ILMU KOMPUTER UNIVERSITAS KOMPUTER INDONESIA 2012

Hasil pengamatan uji laboratorium 15 detik pertama tentang terlarutnya zat obat dalam sistem peredaran darah makhluk hidup diperoleh data seperti yang tertulis pada tabel sebelah kanan. Jika suatu pemodelan matematis dari data pengamatan tersebut ada kecenderungan berbentuk dengan a,b adalah parameter data pengamatan, dan x, y adalah variabel data pengamatan. Maka

(i)

Waktu(detik) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Banyaknya Zat Obat Terlarut (mg) 1.02 0.667 0.367 0.278 0.237 0.187 0.155 0.156 0.142 0.111 0.12 0.097 0.099 0.089 0.079

Tentukan uraian verifikasi matematis dengan linierisasi untuk pembentukan model tersebut agar metode regresi linier dapat dilakukan Perkiraan persamaan umum sederhana untuk model hiperbola ini dapat dituliskan dalam bentuk :

Atau jika tidak ada Y yang bernilai nol dapat ditulis menjadi:

(ii)

Bagaimana anda menghitung parameter a dan b dengan metode regresinya Koefisien-koefisien adan b dapat dihitung seperti pada model garis lurus dengan rumus

(iii)

Berdasarkan (ii), tentukan nilai parameter a dan b untuk model tersebut

1/y

X2

X/Y

Y’

ERROR

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

banyak nya zat obat terlarut 1.02 0.667 0.367 0.278 0.237 0.187 0.155 0.156 0.142 0.111 0.12 0.097 0.099 0.089 0.079

0.980392 1.49925 2.724796 3.597122 4.219409 5.347594 6.451613 6.410256 7.042254 9.009009 8.333333 10.30928 10.10101 11.23596 12.65823

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225

0.980392 2.998501 8.174387 14.38849 21.09705 32.08556 45.16129 51.28205 63.38028 90.09009 91.66667 123.7113 131.3131 157.3034 189.8734

1.249219 -0.03993 -0.01965 -0.01303 -0.00975 -0.00779 -0.00648 -0.00555 -0.00486 -0.00431 -0.00388 -0.00353 -0.00323 -0.00298 -0.00277

0.229219 0.62707 0.34735 0.26497 0.22725 0.17921 0.14852 0.15045 0.13714 0.10669 0.11612 0.09347 0.09577 0.08602 0.07623

∑=120

∑=3.804

∑=99.9195

∑=1240

∑=1023.506

∑=1.121473

∑=2.885479

waktu(detik)

a=

(

)(

) (

)(

(

) (

)

)

a = 26,6452 b=

(

) ( (

b= -25,8447

) (

)( )

)

(iv)

Validasi model yang anda buat dengan menghitung data pengamatan melalui model tersebut = =1,249219

( )

waktu(detik) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ∑=120 (v)

Y^ 1.249219 -0.03993 -0.01965 -0.01303 -0.00975 -0.00779 -0.00648 -0.00555 -0.00486 -0.00431 -0.00388 -0.00353 -0.00323 -0.00298 -0.00277 ∑=1.121473

Gambarkan grafik data pengamatan model

yang sebenarnya dan data pengamatan

1.4 1.2 1 0.8 model nyata

0.6

data model

0.4 0.2 0 -0.2

0

5

10

15

20

(vi)

Simulasikan melalui model untuk memperkirakan berapa milligram(mg) zat obat tersebut sebelum dilarutkan Karena zat sebelum dilarutkan maka nilai X= 0 = = 0,037530212

( )

Screenshoot Program Tampilan Utama

Tabel Berisi Data Pengamatan Setelah Menekan Tombol Mulai

Hasil Perhitungan Kuadrat Terkecil Pada Tabel Setelah Menekan Tombol Proses Kuadrat Terkecil

Hasil validasi model yang ditunjukkan pada kolom y^ dan error dan hasil perhitungan perkiraan jumlah miligram zat obat sebelum dilarutkan pada text field setelah menekan tombol validasi model

Diagram Pencar Data Pengamatan Ditampilkan Setelah Menekan Tombol Grafik Pengamatan

Diagram Pencar Data Model Ditampilkan Setelah Menekan Tombol Grafik Model

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

Listing Program /* * To change this template, choose Tools | Templates * and open the template in the editor. */ package TugasBesar; import javax.swing.table.DefaultTableModel; import javax.swing.table.TableColumn; import javax.swing.*; /** * * @author irwansyahazniel */ public class Pemosi extends javax.swing.JFrame { DefaultTableModel tableModelPengamatan; Double[][] semuaData; Object[] judulKolom; int baris,kolom,inputBaris,inputKolom,inputBarisSigma,inputKolomSigma; double kuadratTerkecilA, kuadratTerkecilB,sebelumLarut; GrafikDataPengamatan grafikDataPengamatan; GrafikDataModel grafikDataModel; /** * Creates new form TampilanUtama */ public Pemosi() { initComponents(); }

42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

public void awal(){ //Inisialisasi Tabel Data Pengamatan judulKolom = new Object[]{"Waktu (Detik)","Banyaknya Obat Yang Terlarut", "1/y", "x2", "X/Y", "Y^", "Error"}; semuaData = new Double[][]{{1.0,1.02,0.0,0.0,0.0,0.0,0.0}, {2.0,0.667,0.0,0.0,0.0,0.0,0.0}, {3.0,0.367,0.0,0.0,0.0,0.0,0.0}, {4.0,0.278,0.0,0.0,0.0,0.0,0.0}, {5.0,0.237,0.0,0.0,0.0,0.0,0.0}, {6.0,0.187,0.0,0.0,0.0,0.0,0.0}, {7.0,0.155,0.0,0.0,0.0,0.0,0.0}, {8.0,0.156,0.0,0.0,0.0,0.0,0.0}, {9.0,0.142,0.0,0.0,0.0,0.0,0.0}, {10.0,0.111,0.0,0.0,0.0,0.0,0.0}, {11.0,0.12,0.0,0.0,0.0,0.0,0.0}, {12.0,0.097,0.0,0.0,0.0,0.0,0.0}, {13.0,0.099,0.0,0.0,0.0,0.0,0.0}, {14.0,0.089,0.0,0.0,0.0,0.0,0.0}, {15.0,0.079,0.0,0.0,0.0,0.0,0.0}, {0.0,0.0,0.0,0.0,0.0,0.0,0.0}}; tableModelPengamatan = new DefaultTableModel(semuaData, judulKolom); tabelPengamatan.setModel(tableModelPengamatan); TableColumn column = null; for (int i = 0; i < judulKolom.length; i++) { column = tabelPengamatan.getColumnModel().getColumn(i); if (i == 0) { column.setPreferredWidth(250); }else if (i == 1) { column.setPreferredWidth(600); }else if (i == 2) { column.setPreferredWidth(600); }else if (i == 3) { column.setPreferredWidth(200); }else if (i == 4) { column.setPreferredWidth(600); }else if (i == 5) { column.setPreferredWidth(600);

83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123

}else if (i == 6) { column.setPreferredWidth(600); } } //Perhitungan Sigma x baris = 0; kolom = 0; inputBaris = 15; inputKolom = 0; double sigmaX = 0; for (int a=0;a