SlideShare a Scribd company logo
1 of 40
Download to read offline
METODE PENELITIAN
Penelitian Pemodelan Komputer 1
Pertemuan 9
2
◼ A mathematical model is central to
most computational scientific research.
◼ Other terms often used in connection
with mathematical modeling are
• Computer modeling
• Computer simulation
• Computational mathematics
• Scientific Computation
• Mathematic Modeling
Computer Modeling & Simulation
3
1. Creates a mathematical representation of
some phenomenon to better understand it.
2. Matches observation with symbolic
representation.
3. Informs theory and explanation.
The success of a mathematical model depends on how
easily it can be used, and how accurately it predicts and
how well it explains the phenomenon being studied.
Computer Modeling & Simulation
Computer Simulations
◼Computer simulation is the process of making
a computer behave the same as ...whatever it is
we are interested in.
• Atoms
• Cooling metal alloy
• A society of voters
• Climate change
• A galaxy
4
Computer Simulations
◼Simulations have applications across a range
of disciplines:
◼Physics – solids, gases, fluids, solar systems
◼Chemistry – molecular dynamics
◼Biology – gene networks, predator-prey populations
◼Sociology – socio networks, opinion propagation
◼Technology – internet traffic, local networks
◼Management – queuing, workflow models
◼Finance & Economics – stock markets, supply-
demand
◼Agriculture – pest outbreak, rainy or drought season
5
Computer Simulations
◼Computer simulations allow us to observe the
behaviour of these systems at (relatively) low
cost.
◼Other methods of investigating these systems
may involve complicated theoretical research or
experimental research with potentially
expensive equipment.
6
Computer Simulations
There are some definitions of
simulations:
◼"The representation of the dynamic behaviour of the
system by moving it from state to state in accordance
with well-defined operating rules." – A. Alan B. Pritsker
(1984)
◼"We can therefore define simulation as the technique
of solving problems by the observation of the
performance, over the time, of a dynamic model of the
system." – Bernard P. Zeigler (1976)
◼"A simulation is a method for implementing a model."
– Defense Acquisition University
7
Computer Simulations
◼To create a computer simulation to
approximate a system, a model of that system
must first be made. These are most often
mathematical models.
◼"A model is a description of some system intended to predict what
happens if certain actions are taken"
– Bratley, Bennet & Schrage (1987)
8
Models
◼Modelling is a large discipline in itself and
creating a system requires a lot of mathematical
ability and understanding of the system.
◼Models are usually composed of variables and
relationships between them. Exactly what these
variables represent and what the relationships
between them are can vary.
9
Models
The variables of the model must represent the
state of the system. The state is split into
different components to represent the different
parts of the system. These are sometimes
called model components.
For example:
A car in a traffic simulator may have a position,
a size and a velocity.
10
Models
When using computer simulations, it is important to
understand the limitations of the model you are using. A
simulation (no matter how accurate) cannot provide
useful results if the model is not suitable for the system
you are studying.
A model is considered valid if the system it describes
sufficiently near to the real system.
11
What is Simulation?
A Simulation of a system is the operation of a model, which is
a representation of that system.
The model is amenable to manipulation which would be
impossible, too expensive, or too impractical to perform on
the system which it portrays.
The operation of the model can be studied, and, from this,
properties concerning the behavior of the actual system can
be inferred.
Applications:
1. Designing and analyzing manufacturing
systems
2. Evaluating H/W and S/W requirements
for a computer system
3. Evaluating a new military weapons
system or tactics
4. Determining ordering policies for an
inventory system
5. Designing communications systems and
message protocols for them
Applications:(continued)
Designing and operating transportation
facilities such as freeways, airports, subways,
or ports
Evaluating designs for service organizations
such as hospitals, post offices, or fast-food
restaurants
Analyzing financial or economic systems
Perbedaan :
◼A model
• An abstraction of the system being studied
that we claim behaves much like the original
◼Computer simulation
• A physical system is modeled as a set of
mathematical equations and/or algorithmic
procedures
Perbedaan :
◼ Computer simulation (continued)
• Model is translated into a high-level language and
executed on the Von Neumann computer
◼ Computational models
• Also called simulation models
• Used to
–Design new systems
–Study and improve the behavior of existing
systems
Computational models (continued)
• Allow the use of an interactive design
methodology (sometimes called
computational steering)
• Used in most branches of science and
engineering
Using a Simulation in an
Interactive Design
Environment
Matematical Modeling
Models are used not only in the natural sciences (such as
physics, biology, earth science, meteorology) and
engineering/architecture disciplines, but also in the social
sciences (such as economics, psychology, sociology and
political science). Here is a list:
1. Physical Models
2. Analogic Models
3. Provisional Theories
4. Maps and Drawings
5. Mathematical and symbolic models
MATHEMATICAL MODELING
Definitions
A mathematical model is a representation, in
mathematical terms, of certain aspects of a non-
mathematical system.
A mathematical model is a set of mathematical
equations that are intended to capture the effect of
certain system variables on certain other system
variables.
A model may be prescriptive or illustrative, but,
above all, it must be useful !
A mathematical model is a description of a system using
mathematical concepts and language. The process of
developing a mathematical model is termed mathematical
modelling.
Mathematical models are used not only in the natural
sciences (such as physics, biology, earth science,
meteorology) and engineering disciplines (e.g. computer
science, artificial intelligence), but also in the social sciences
(such as economics, psychology, sociology and political
science); physicists, engineers, statisticians, operations
research analysts and economists use mathematical models
most extensively.
A mathematical model usually describes a system by a set of
variables and a set of equations that establish relationships
between the variables.
WHY MATH MODELING FOR PROCESS SYSTEMS?
◼ Understand the problem: Why does one
need a model?
◼ Is it:
➢to design a controller?
➢to analyze the performance of the process?
➢to understand the process better?
➢to simplify the complexity of a system
➢etc.
Mathematics Modeling Cycle
Mathematical
Modeling
A Real-World Problem:
• Model the spread and control of the pest.
• Model manufacturing processes to minimize time-to-market
and cost.
• Model training times to optimize performance in sprints/long
distance running.
Understand current activity and predict future
behavior.
Example: Falling Rock
Determine the motion of a rock dropped from height,
H, above the ground with initial velocity, V.
A discrete model: Find the position and velocity of
the rock at the equally spaced times, t0, t1, t2, …;
e.g., t0 = 0 sec., t1 = 1 sec., t2 = 2 sec., etc.
|______|______|____________|______
t0 t1 t2 … tn

Mathematical
Modeling
Simplify → Working Model:
Identify and select factors that
describe important aspects of
the Real World Problem; deter-
mine those factors that can be
neglected.
• Determine governing principles, physical laws.
• Identify model variables; focus on how they are related.
• State simplifying assumptions.
Example: Falling Rock
◼ Governing principles: d = v*t and v = a*t.
◼ Simplifying assumptions:
• Gravity is the only force acting on the body.
• Flat earth.
• No drag (air resistance).
• Rock’s position and velocity above the ground will be
modeled at discrete times (t0, t1, t2, …) until rock hits
the ground.
Mathematical
Modeling
Abstract → Mathematical
Model: Express the Working
Model in mathematical terms;
write down mathematical equations whose
solution describes the Working Model.
There may not be a "best" model; the one to
be used will depend on the questions to be studied.
Example: Falling Rock
v0 v1 v2 … vn
x0 x1 x2 … xn
|______|______|____________|______
t0 t1 t2 … tn
t0 = 0; x0 = H; v0 = V; Δt = ti+1 - ti
t1= t0 + Δt
x1= x0 + (v0*Δt)
v1= v0 - (g*Δt)
t2= t1 + Δt
x2= x1 + (v1*Δt)
v2= v1 - (g*Δt)
…
Mathematical
Modeling
Program → Computational
Model: Implement Mathematical Model in
“computer code”.
If model is simple enough, it may be solved
analytically; otherwise, a computer program is
required.
Example: Falling Rock
Pseudo Code
Input
V, initial velocity; H, initial height
g, acceleration due to gravity
Δt, time step; imax, maximum number of steps
Output
ti, t-value at time step i
xi, height at time ti
vi, velocity at time ti
Example: Falling Rock
Initialize
ti = t0 = 0; vi = v0 = V; xi = x0 = H
print ti, xi, vi
Time stepping: i = 1, imax
ti = ti + Δt
xi = xi - vi*Δt
vi = vi + g*Δt
print ti, xi, vi
if (xi <= 0), xi = 0; quit
Mathematical
Modeling
Simulate → Conclusions: Execute “computer code”
to obtain Results. Formulate Conclusions.
• Verify your computer program; use check cases.
• Graphs, charts, and other visualization tools are useful in
summarizing results and drawing conclusions.
Mathematical
Modeling
Interpret Conclusions and compare with Real
World Problem behavior.
• If model results do not “agree” with physical reality or
experimental data, reexamine the Working Model and repeat
modeling steps.
• Usually, modeling process proceeds through several
iterations until model is“acceptable”.
Example: Falling Rock
To create a more more realistic model of
a falling rock, some of the simplifying
assumptions could be dropped:
• Incorporate air resistance, depends on
shape of rock.
• Improve discrete model: approximate
velocities in the midpoint of time intervals
instead of the beginning.
• Reduce the size of Δt.
Mathematics Modeling Cycle
Daftar Pustaka
◼ Mathematical Modeling, Summer Teacher Institute, 2002
Questions?
ANOVA
TERIMA KASIH

More Related Content

Similar to Materi 10 - Penelitian Pemodelan Komputer.pdf

Introduction to simulation.pdf
Introduction to simulation.pdfIntroduction to simulation.pdf
Introduction to simulation.pdfnadimhossain24
 
Mathematical Modeling
Mathematical ModelingMathematical Modeling
Mathematical ModelingMohsen EM
 
Mathematical models and algorithms challenges
Mathematical models and algorithms challengesMathematical models and algorithms challenges
Mathematical models and algorithms challengesijctcm
 
Machine learning ppt unit one syllabuspptx
Machine learning ppt unit one syllabuspptxMachine learning ppt unit one syllabuspptx
Machine learning ppt unit one syllabuspptxVenkateswaraBabuRavi
 
System Modeling & Simulation Introduction
System Modeling & Simulation  IntroductionSystem Modeling & Simulation  Introduction
System Modeling & Simulation IntroductionSharmilaChidaravalli
 
Cs854 lecturenotes01
Cs854 lecturenotes01Cs854 lecturenotes01
Cs854 lecturenotes01Mehmet Çelik
 
Discreate Event Simulation_PPT1-R0.ppt
Discreate Event Simulation_PPT1-R0.pptDiscreate Event Simulation_PPT1-R0.ppt
Discreate Event Simulation_PPT1-R0.pptdiklatMSU
 
3. 2. decision making
3. 2. decision making3. 2. decision making
3. 2. decision makingJamshid khan
 
Modeling & Simulation Lecture Notes
Modeling & Simulation Lecture NotesModeling & Simulation Lecture Notes
Modeling & Simulation Lecture NotesFellowBuddy.com
 
Introduction to System, Simulation and Model
Introduction to System, Simulation and ModelIntroduction to System, Simulation and Model
Introduction to System, Simulation and ModelMd. Hasan Imam Bijoy
 
Operations Research - Models
Operations Research - ModelsOperations Research - Models
Operations Research - ModelsSundar B N
 
A Comparison of Traditional Simulation and MSAL (6-3-2015)
A Comparison of Traditional Simulation and MSAL (6-3-2015)A Comparison of Traditional Simulation and MSAL (6-3-2015)
A Comparison of Traditional Simulation and MSAL (6-3-2015)Bob Garrett
 
System modeling and simulation full notes by sushma shetty (www.vtulife.com)
System modeling and simulation full notes by sushma shetty (www.vtulife.com)System modeling and simulation full notes by sushma shetty (www.vtulife.com)
System modeling and simulation full notes by sushma shetty (www.vtulife.com)Vivek Maurya
 
Statistical learning vs. Machine Learning
Statistical learning vs. Machine LearningStatistical learning vs. Machine Learning
Statistical learning vs. Machine LearningAtanu Ray
 
Md simulation and stochastic simulation
Md simulation and stochastic simulationMd simulation and stochastic simulation
Md simulation and stochastic simulationAbdulAhad358
 
Models of spatial process by sushant
Models of spatial process by sushantModels of spatial process by sushant
Models of spatial process by sushantsushantsawant13
 

Similar to Materi 10 - Penelitian Pemodelan Komputer.pdf (20)

lecture 1.pptx
lecture 1.pptxlecture 1.pptx
lecture 1.pptx
 
SIMULATION.pdf
SIMULATION.pdfSIMULATION.pdf
SIMULATION.pdf
 
Introduction to simulation.pdf
Introduction to simulation.pdfIntroduction to simulation.pdf
Introduction to simulation.pdf
 
Mathematical Modeling
Mathematical ModelingMathematical Modeling
Mathematical Modeling
 
Mathematical models and algorithms challenges
Mathematical models and algorithms challengesMathematical models and algorithms challenges
Mathematical models and algorithms challenges
 
Machine learning ppt unit one syllabuspptx
Machine learning ppt unit one syllabuspptxMachine learning ppt unit one syllabuspptx
Machine learning ppt unit one syllabuspptx
 
System Modeling & Simulation Introduction
System Modeling & Simulation  IntroductionSystem Modeling & Simulation  Introduction
System Modeling & Simulation Introduction
 
Cs854 lecturenotes01
Cs854 lecturenotes01Cs854 lecturenotes01
Cs854 lecturenotes01
 
Discreate Event Simulation_PPT1-R0.ppt
Discreate Event Simulation_PPT1-R0.pptDiscreate Event Simulation_PPT1-R0.ppt
Discreate Event Simulation_PPT1-R0.ppt
 
3. 2. decision making
3. 2. decision making3. 2. decision making
3. 2. decision making
 
Modeling & Simulation Lecture Notes
Modeling & Simulation Lecture NotesModeling & Simulation Lecture Notes
Modeling & Simulation Lecture Notes
 
Introduction to System, Simulation and Model
Introduction to System, Simulation and ModelIntroduction to System, Simulation and Model
Introduction to System, Simulation and Model
 
Operations Research - Models
Operations Research - ModelsOperations Research - Models
Operations Research - Models
 
A Comparison of Traditional Simulation and MSAL (6-3-2015)
A Comparison of Traditional Simulation and MSAL (6-3-2015)A Comparison of Traditional Simulation and MSAL (6-3-2015)
A Comparison of Traditional Simulation and MSAL (6-3-2015)
 
calculus assignment of math
calculus assignment of mathcalculus assignment of math
calculus assignment of math
 
System modeling and simulation full notes by sushma shetty (www.vtulife.com)
System modeling and simulation full notes by sushma shetty (www.vtulife.com)System modeling and simulation full notes by sushma shetty (www.vtulife.com)
System modeling and simulation full notes by sushma shetty (www.vtulife.com)
 
Statistical learning vs. Machine Learning
Statistical learning vs. Machine LearningStatistical learning vs. Machine Learning
Statistical learning vs. Machine Learning
 
MODELING & SIMULATION.docx
MODELING & SIMULATION.docxMODELING & SIMULATION.docx
MODELING & SIMULATION.docx
 
Md simulation and stochastic simulation
Md simulation and stochastic simulationMd simulation and stochastic simulation
Md simulation and stochastic simulation
 
Models of spatial process by sushant
Models of spatial process by sushantModels of spatial process by sushant
Models of spatial process by sushant
 

More from MahesaRioAditya

Materi 11 - Penelitian Pemodelan Komputer.pdf
Materi 11 - Penelitian Pemodelan Komputer.pdfMateri 11 - Penelitian Pemodelan Komputer.pdf
Materi 11 - Penelitian Pemodelan Komputer.pdfMahesaRioAditya
 
Materi 6 - Tinjauan Pustaka.pdf
Materi 6 - Tinjauan Pustaka.pdfMateri 6 - Tinjauan Pustaka.pdf
Materi 6 - Tinjauan Pustaka.pdfMahesaRioAditya
 
Materi 13 - Teknik Presentasi 2.pdf
Materi 13 - Teknik Presentasi 2.pdfMateri 13 - Teknik Presentasi 2.pdf
Materi 13 - Teknik Presentasi 2.pdfMahesaRioAditya
 
Materi 7 - Teknik Sampling.pdf
Materi 7 - Teknik Sampling.pdfMateri 7 - Teknik Sampling.pdf
Materi 7 - Teknik Sampling.pdfMahesaRioAditya
 
Materi 12 - Teknik Presentasi.pdf
Materi 12 - Teknik Presentasi.pdfMateri 12 - Teknik Presentasi.pdf
Materi 12 - Teknik Presentasi.pdfMahesaRioAditya
 
Materi 14 - Reference Manager (mendeley).pdf
Materi 14 - Reference Manager (mendeley).pdfMateri 14 - Reference Manager (mendeley).pdf
Materi 14 - Reference Manager (mendeley).pdfMahesaRioAditya
 
Materi 4 - Penelitian.pdf
Materi 4 - Penelitian.pdfMateri 4 - Penelitian.pdf
Materi 4 - Penelitian.pdfMahesaRioAditya
 
Materi 8 - Teknik Sampling 2.pdf
Materi 8 - Teknik Sampling 2.pdfMateri 8 - Teknik Sampling 2.pdf
Materi 8 - Teknik Sampling 2.pdfMahesaRioAditya
 
Materi 9 - Makalah Ilmiah.pdf
Materi 9 - Makalah Ilmiah.pdfMateri 9 - Makalah Ilmiah.pdf
Materi 9 - Makalah Ilmiah.pdfMahesaRioAditya
 
Materi 3 - Perumusan Masalah.pdf
Materi 3 - Perumusan Masalah.pdfMateri 3 - Perumusan Masalah.pdf
Materi 3 - Perumusan Masalah.pdfMahesaRioAditya
 
Materi 5 - Tinjauan Pustaka.pdf
Materi 5 - Tinjauan Pustaka.pdfMateri 5 - Tinjauan Pustaka.pdf
Materi 5 - Tinjauan Pustaka.pdfMahesaRioAditya
 
Materi 15 - Budaya Menulis.pdf
Materi 15 - Budaya Menulis.pdfMateri 15 - Budaya Menulis.pdf
Materi 15 - Budaya Menulis.pdfMahesaRioAditya
 
Materi 16 - Tata Cara Penyusunan.pdf
Materi 16 - Tata Cara Penyusunan.pdfMateri 16 - Tata Cara Penyusunan.pdf
Materi 16 - Tata Cara Penyusunan.pdfMahesaRioAditya
 
Materi 2 - Unsur-unsur proposal penelitian.pdf
Materi 2 - Unsur-unsur proposal penelitian.pdfMateri 2 - Unsur-unsur proposal penelitian.pdf
Materi 2 - Unsur-unsur proposal penelitian.pdfMahesaRioAditya
 

More from MahesaRioAditya (14)

Materi 11 - Penelitian Pemodelan Komputer.pdf
Materi 11 - Penelitian Pemodelan Komputer.pdfMateri 11 - Penelitian Pemodelan Komputer.pdf
Materi 11 - Penelitian Pemodelan Komputer.pdf
 
Materi 6 - Tinjauan Pustaka.pdf
Materi 6 - Tinjauan Pustaka.pdfMateri 6 - Tinjauan Pustaka.pdf
Materi 6 - Tinjauan Pustaka.pdf
 
Materi 13 - Teknik Presentasi 2.pdf
Materi 13 - Teknik Presentasi 2.pdfMateri 13 - Teknik Presentasi 2.pdf
Materi 13 - Teknik Presentasi 2.pdf
 
Materi 7 - Teknik Sampling.pdf
Materi 7 - Teknik Sampling.pdfMateri 7 - Teknik Sampling.pdf
Materi 7 - Teknik Sampling.pdf
 
Materi 12 - Teknik Presentasi.pdf
Materi 12 - Teknik Presentasi.pdfMateri 12 - Teknik Presentasi.pdf
Materi 12 - Teknik Presentasi.pdf
 
Materi 14 - Reference Manager (mendeley).pdf
Materi 14 - Reference Manager (mendeley).pdfMateri 14 - Reference Manager (mendeley).pdf
Materi 14 - Reference Manager (mendeley).pdf
 
Materi 4 - Penelitian.pdf
Materi 4 - Penelitian.pdfMateri 4 - Penelitian.pdf
Materi 4 - Penelitian.pdf
 
Materi 8 - Teknik Sampling 2.pdf
Materi 8 - Teknik Sampling 2.pdfMateri 8 - Teknik Sampling 2.pdf
Materi 8 - Teknik Sampling 2.pdf
 
Materi 9 - Makalah Ilmiah.pdf
Materi 9 - Makalah Ilmiah.pdfMateri 9 - Makalah Ilmiah.pdf
Materi 9 - Makalah Ilmiah.pdf
 
Materi 3 - Perumusan Masalah.pdf
Materi 3 - Perumusan Masalah.pdfMateri 3 - Perumusan Masalah.pdf
Materi 3 - Perumusan Masalah.pdf
 
Materi 5 - Tinjauan Pustaka.pdf
Materi 5 - Tinjauan Pustaka.pdfMateri 5 - Tinjauan Pustaka.pdf
Materi 5 - Tinjauan Pustaka.pdf
 
Materi 15 - Budaya Menulis.pdf
Materi 15 - Budaya Menulis.pdfMateri 15 - Budaya Menulis.pdf
Materi 15 - Budaya Menulis.pdf
 
Materi 16 - Tata Cara Penyusunan.pdf
Materi 16 - Tata Cara Penyusunan.pdfMateri 16 - Tata Cara Penyusunan.pdf
Materi 16 - Tata Cara Penyusunan.pdf
 
Materi 2 - Unsur-unsur proposal penelitian.pdf
Materi 2 - Unsur-unsur proposal penelitian.pdfMateri 2 - Unsur-unsur proposal penelitian.pdf
Materi 2 - Unsur-unsur proposal penelitian.pdf
 

Recently uploaded

ESP 4-EDITED.pdfmmcncncncmcmmnmnmncnmncmnnjvnnv
ESP 4-EDITED.pdfmmcncncncmcmmnmnmncnmncmnnjvnnvESP 4-EDITED.pdfmmcncncncmcmmnmnmncnmncmnnjvnnv
ESP 4-EDITED.pdfmmcncncncmcmmnmnmncnmncmnnjvnnvRicaMaeCastro1
 
Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...
Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...
Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...Osopher
 
Comparative Literature in India by Amiya dev.pptx
Comparative Literature in India by Amiya dev.pptxComparative Literature in India by Amiya dev.pptx
Comparative Literature in India by Amiya dev.pptxAvaniJani1
 
ICS 2208 Lecture Slide Notes for Topic 6
ICS 2208 Lecture Slide Notes for Topic 6ICS 2208 Lecture Slide Notes for Topic 6
ICS 2208 Lecture Slide Notes for Topic 6Vanessa Camilleri
 
Q-Factor HISPOL Quiz-6th April 2024, Quiz Club NITW
Q-Factor HISPOL Quiz-6th April 2024, Quiz Club NITWQ-Factor HISPOL Quiz-6th April 2024, Quiz Club NITW
Q-Factor HISPOL Quiz-6th April 2024, Quiz Club NITWQuiz Club NITW
 
Team Lead Succeed – Helping you and your team achieve high-performance teamwo...
Team Lead Succeed – Helping you and your team achieve high-performance teamwo...Team Lead Succeed – Helping you and your team achieve high-performance teamwo...
Team Lead Succeed – Helping you and your team achieve high-performance teamwo...Association for Project Management
 
ClimART Action | eTwinning Project
ClimART Action    |    eTwinning ProjectClimART Action    |    eTwinning Project
ClimART Action | eTwinning Projectjordimapav
 
6 ways Samsung’s Interactive Display powered by Android changes the classroom
6 ways Samsung’s Interactive Display powered by Android changes the classroom6 ways Samsung’s Interactive Display powered by Android changes the classroom
6 ways Samsung’s Interactive Display powered by Android changes the classroomSamsung Business USA
 
Transaction Management in Database Management System
Transaction Management in Database Management SystemTransaction Management in Database Management System
Transaction Management in Database Management SystemChristalin Nelson
 
Q-Factor General Quiz-7th April 2024, Quiz Club NITW
Q-Factor General Quiz-7th April 2024, Quiz Club NITWQ-Factor General Quiz-7th April 2024, Quiz Club NITW
Q-Factor General Quiz-7th April 2024, Quiz Club NITWQuiz Club NITW
 
Mythology Quiz-4th April 2024, Quiz Club NITW
Mythology Quiz-4th April 2024, Quiz Club NITWMythology Quiz-4th April 2024, Quiz Club NITW
Mythology Quiz-4th April 2024, Quiz Club NITWQuiz Club NITW
 
Scientific Writing :Research Discourse
Scientific  Writing :Research  DiscourseScientific  Writing :Research  Discourse
Scientific Writing :Research DiscourseAnita GoswamiGiri
 
How to Uninstall a Module in Odoo 17 Using Command Line
How to Uninstall a Module in Odoo 17 Using Command LineHow to Uninstall a Module in Odoo 17 Using Command Line
How to Uninstall a Module in Odoo 17 Using Command LineCeline George
 
Congestive Cardiac Failure..presentation
Congestive Cardiac Failure..presentationCongestive Cardiac Failure..presentation
Congestive Cardiac Failure..presentationdeepaannamalai16
 
Sulphonamides, mechanisms and their uses
Sulphonamides, mechanisms and their usesSulphonamides, mechanisms and their uses
Sulphonamides, mechanisms and their usesVijayaLaxmi84
 

Recently uploaded (20)

ESP 4-EDITED.pdfmmcncncncmcmmnmnmncnmncmnnjvnnv
ESP 4-EDITED.pdfmmcncncncmcmmnmnmncnmncmnnjvnnvESP 4-EDITED.pdfmmcncncncmcmmnmnmncnmncmnnjvnnv
ESP 4-EDITED.pdfmmcncncncmcmmnmnmncnmncmnnjvnnv
 
Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...
Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...
Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...
 
Comparative Literature in India by Amiya dev.pptx
Comparative Literature in India by Amiya dev.pptxComparative Literature in India by Amiya dev.pptx
Comparative Literature in India by Amiya dev.pptx
 
ICS 2208 Lecture Slide Notes for Topic 6
ICS 2208 Lecture Slide Notes for Topic 6ICS 2208 Lecture Slide Notes for Topic 6
ICS 2208 Lecture Slide Notes for Topic 6
 
Faculty Profile prashantha K EEE dept Sri Sairam college of Engineering
Faculty Profile prashantha K EEE dept Sri Sairam college of EngineeringFaculty Profile prashantha K EEE dept Sri Sairam college of Engineering
Faculty Profile prashantha K EEE dept Sri Sairam college of Engineering
 
Q-Factor HISPOL Quiz-6th April 2024, Quiz Club NITW
Q-Factor HISPOL Quiz-6th April 2024, Quiz Club NITWQ-Factor HISPOL Quiz-6th April 2024, Quiz Club NITW
Q-Factor HISPOL Quiz-6th April 2024, Quiz Club NITW
 
Team Lead Succeed – Helping you and your team achieve high-performance teamwo...
Team Lead Succeed – Helping you and your team achieve high-performance teamwo...Team Lead Succeed – Helping you and your team achieve high-performance teamwo...
Team Lead Succeed – Helping you and your team achieve high-performance teamwo...
 
ClimART Action | eTwinning Project
ClimART Action    |    eTwinning ProjectClimART Action    |    eTwinning Project
ClimART Action | eTwinning Project
 
6 ways Samsung’s Interactive Display powered by Android changes the classroom
6 ways Samsung’s Interactive Display powered by Android changes the classroom6 ways Samsung’s Interactive Display powered by Android changes the classroom
6 ways Samsung’s Interactive Display powered by Android changes the classroom
 
Transaction Management in Database Management System
Transaction Management in Database Management SystemTransaction Management in Database Management System
Transaction Management in Database Management System
 
Q-Factor General Quiz-7th April 2024, Quiz Club NITW
Q-Factor General Quiz-7th April 2024, Quiz Club NITWQ-Factor General Quiz-7th April 2024, Quiz Club NITW
Q-Factor General Quiz-7th April 2024, Quiz Club NITW
 
Mythology Quiz-4th April 2024, Quiz Club NITW
Mythology Quiz-4th April 2024, Quiz Club NITWMythology Quiz-4th April 2024, Quiz Club NITW
Mythology Quiz-4th April 2024, Quiz Club NITW
 
Paradigm shift in nursing research by RS MEHTA
Paradigm shift in nursing research by RS MEHTAParadigm shift in nursing research by RS MEHTA
Paradigm shift in nursing research by RS MEHTA
 
Scientific Writing :Research Discourse
Scientific  Writing :Research  DiscourseScientific  Writing :Research  Discourse
Scientific Writing :Research Discourse
 
Introduction to Research ,Need for research, Need for design of Experiments, ...
Introduction to Research ,Need for research, Need for design of Experiments, ...Introduction to Research ,Need for research, Need for design of Experiments, ...
Introduction to Research ,Need for research, Need for design of Experiments, ...
 
How to Uninstall a Module in Odoo 17 Using Command Line
How to Uninstall a Module in Odoo 17 Using Command LineHow to Uninstall a Module in Odoo 17 Using Command Line
How to Uninstall a Module in Odoo 17 Using Command Line
 
Congestive Cardiac Failure..presentation
Congestive Cardiac Failure..presentationCongestive Cardiac Failure..presentation
Congestive Cardiac Failure..presentation
 
Sulphonamides, mechanisms and their uses
Sulphonamides, mechanisms and their usesSulphonamides, mechanisms and their uses
Sulphonamides, mechanisms and their uses
 
Chi-Square Test Non Parametric Test Categorical Variable
Chi-Square Test Non Parametric Test Categorical VariableChi-Square Test Non Parametric Test Categorical Variable
Chi-Square Test Non Parametric Test Categorical Variable
 
Plagiarism,forms,understand about plagiarism,avoid plagiarism,key significanc...
Plagiarism,forms,understand about plagiarism,avoid plagiarism,key significanc...Plagiarism,forms,understand about plagiarism,avoid plagiarism,key significanc...
Plagiarism,forms,understand about plagiarism,avoid plagiarism,key significanc...
 

Materi 10 - Penelitian Pemodelan Komputer.pdf

  • 1. METODE PENELITIAN Penelitian Pemodelan Komputer 1 Pertemuan 9
  • 2. 2 ◼ A mathematical model is central to most computational scientific research. ◼ Other terms often used in connection with mathematical modeling are • Computer modeling • Computer simulation • Computational mathematics • Scientific Computation • Mathematic Modeling Computer Modeling & Simulation
  • 3. 3 1. Creates a mathematical representation of some phenomenon to better understand it. 2. Matches observation with symbolic representation. 3. Informs theory and explanation. The success of a mathematical model depends on how easily it can be used, and how accurately it predicts and how well it explains the phenomenon being studied. Computer Modeling & Simulation
  • 4. Computer Simulations ◼Computer simulation is the process of making a computer behave the same as ...whatever it is we are interested in. • Atoms • Cooling metal alloy • A society of voters • Climate change • A galaxy 4
  • 5. Computer Simulations ◼Simulations have applications across a range of disciplines: ◼Physics – solids, gases, fluids, solar systems ◼Chemistry – molecular dynamics ◼Biology – gene networks, predator-prey populations ◼Sociology – socio networks, opinion propagation ◼Technology – internet traffic, local networks ◼Management – queuing, workflow models ◼Finance & Economics – stock markets, supply- demand ◼Agriculture – pest outbreak, rainy or drought season 5
  • 6. Computer Simulations ◼Computer simulations allow us to observe the behaviour of these systems at (relatively) low cost. ◼Other methods of investigating these systems may involve complicated theoretical research or experimental research with potentially expensive equipment. 6
  • 7. Computer Simulations There are some definitions of simulations: ◼"The representation of the dynamic behaviour of the system by moving it from state to state in accordance with well-defined operating rules." – A. Alan B. Pritsker (1984) ◼"We can therefore define simulation as the technique of solving problems by the observation of the performance, over the time, of a dynamic model of the system." – Bernard P. Zeigler (1976) ◼"A simulation is a method for implementing a model." – Defense Acquisition University 7
  • 8. Computer Simulations ◼To create a computer simulation to approximate a system, a model of that system must first be made. These are most often mathematical models. ◼"A model is a description of some system intended to predict what happens if certain actions are taken" – Bratley, Bennet & Schrage (1987) 8
  • 9. Models ◼Modelling is a large discipline in itself and creating a system requires a lot of mathematical ability and understanding of the system. ◼Models are usually composed of variables and relationships between them. Exactly what these variables represent and what the relationships between them are can vary. 9
  • 10. Models The variables of the model must represent the state of the system. The state is split into different components to represent the different parts of the system. These are sometimes called model components. For example: A car in a traffic simulator may have a position, a size and a velocity. 10
  • 11. Models When using computer simulations, it is important to understand the limitations of the model you are using. A simulation (no matter how accurate) cannot provide useful results if the model is not suitable for the system you are studying. A model is considered valid if the system it describes sufficiently near to the real system. 11
  • 12. What is Simulation? A Simulation of a system is the operation of a model, which is a representation of that system. The model is amenable to manipulation which would be impossible, too expensive, or too impractical to perform on the system which it portrays. The operation of the model can be studied, and, from this, properties concerning the behavior of the actual system can be inferred.
  • 13. Applications: 1. Designing and analyzing manufacturing systems 2. Evaluating H/W and S/W requirements for a computer system 3. Evaluating a new military weapons system or tactics 4. Determining ordering policies for an inventory system 5. Designing communications systems and message protocols for them
  • 14. Applications:(continued) Designing and operating transportation facilities such as freeways, airports, subways, or ports Evaluating designs for service organizations such as hospitals, post offices, or fast-food restaurants Analyzing financial or economic systems
  • 15. Perbedaan : ◼A model • An abstraction of the system being studied that we claim behaves much like the original ◼Computer simulation • A physical system is modeled as a set of mathematical equations and/or algorithmic procedures
  • 16. Perbedaan : ◼ Computer simulation (continued) • Model is translated into a high-level language and executed on the Von Neumann computer ◼ Computational models • Also called simulation models • Used to –Design new systems –Study and improve the behavior of existing systems
  • 17. Computational models (continued) • Allow the use of an interactive design methodology (sometimes called computational steering) • Used in most branches of science and engineering
  • 18. Using a Simulation in an Interactive Design Environment
  • 19. Matematical Modeling Models are used not only in the natural sciences (such as physics, biology, earth science, meteorology) and engineering/architecture disciplines, but also in the social sciences (such as economics, psychology, sociology and political science). Here is a list: 1. Physical Models 2. Analogic Models 3. Provisional Theories 4. Maps and Drawings 5. Mathematical and symbolic models
  • 20. MATHEMATICAL MODELING Definitions A mathematical model is a representation, in mathematical terms, of certain aspects of a non- mathematical system. A mathematical model is a set of mathematical equations that are intended to capture the effect of certain system variables on certain other system variables. A model may be prescriptive or illustrative, but, above all, it must be useful !
  • 21. A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modelling. Mathematical models are used not only in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines (e.g. computer science, artificial intelligence), but also in the social sciences (such as economics, psychology, sociology and political science); physicists, engineers, statisticians, operations research analysts and economists use mathematical models most extensively. A mathematical model usually describes a system by a set of variables and a set of equations that establish relationships between the variables.
  • 22. WHY MATH MODELING FOR PROCESS SYSTEMS? ◼ Understand the problem: Why does one need a model? ◼ Is it: ➢to design a controller? ➢to analyze the performance of the process? ➢to understand the process better? ➢to simplify the complexity of a system ➢etc.
  • 24. Mathematical Modeling A Real-World Problem: • Model the spread and control of the pest. • Model manufacturing processes to minimize time-to-market and cost. • Model training times to optimize performance in sprints/long distance running. Understand current activity and predict future behavior.
  • 25. Example: Falling Rock Determine the motion of a rock dropped from height, H, above the ground with initial velocity, V. A discrete model: Find the position and velocity of the rock at the equally spaced times, t0, t1, t2, …; e.g., t0 = 0 sec., t1 = 1 sec., t2 = 2 sec., etc. |______|______|____________|______ t0 t1 t2 … tn 
  • 26. Mathematical Modeling Simplify → Working Model: Identify and select factors that describe important aspects of the Real World Problem; deter- mine those factors that can be neglected. • Determine governing principles, physical laws. • Identify model variables; focus on how they are related. • State simplifying assumptions.
  • 27. Example: Falling Rock ◼ Governing principles: d = v*t and v = a*t. ◼ Simplifying assumptions: • Gravity is the only force acting on the body. • Flat earth. • No drag (air resistance). • Rock’s position and velocity above the ground will be modeled at discrete times (t0, t1, t2, …) until rock hits the ground.
  • 28. Mathematical Modeling Abstract → Mathematical Model: Express the Working Model in mathematical terms; write down mathematical equations whose solution describes the Working Model. There may not be a "best" model; the one to be used will depend on the questions to be studied.
  • 29. Example: Falling Rock v0 v1 v2 … vn x0 x1 x2 … xn |______|______|____________|______ t0 t1 t2 … tn t0 = 0; x0 = H; v0 = V; Δt = ti+1 - ti t1= t0 + Δt x1= x0 + (v0*Δt) v1= v0 - (g*Δt) t2= t1 + Δt x2= x1 + (v1*Δt) v2= v1 - (g*Δt) …
  • 30. Mathematical Modeling Program → Computational Model: Implement Mathematical Model in “computer code”. If model is simple enough, it may be solved analytically; otherwise, a computer program is required.
  • 31. Example: Falling Rock Pseudo Code Input V, initial velocity; H, initial height g, acceleration due to gravity Δt, time step; imax, maximum number of steps Output ti, t-value at time step i xi, height at time ti vi, velocity at time ti
  • 32. Example: Falling Rock Initialize ti = t0 = 0; vi = v0 = V; xi = x0 = H print ti, xi, vi Time stepping: i = 1, imax ti = ti + Δt xi = xi - vi*Δt vi = vi + g*Δt print ti, xi, vi if (xi <= 0), xi = 0; quit
  • 33. Mathematical Modeling Simulate → Conclusions: Execute “computer code” to obtain Results. Formulate Conclusions. • Verify your computer program; use check cases. • Graphs, charts, and other visualization tools are useful in summarizing results and drawing conclusions.
  • 34. Mathematical Modeling Interpret Conclusions and compare with Real World Problem behavior. • If model results do not “agree” with physical reality or experimental data, reexamine the Working Model and repeat modeling steps. • Usually, modeling process proceeds through several iterations until model is“acceptable”.
  • 35. Example: Falling Rock To create a more more realistic model of a falling rock, some of the simplifying assumptions could be dropped: • Incorporate air resistance, depends on shape of rock. • Improve discrete model: approximate velocities in the midpoint of time intervals instead of the beginning. • Reduce the size of Δt.
  • 37. Daftar Pustaka ◼ Mathematical Modeling, Summer Teacher Institute, 2002
  • 39. ANOVA