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8/10/2019 Introduction System Modeling
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03/09/20
Anna Maria Sri Asih
Department of Mechanical & Industrial EngineeringGadjah Mada University
• Lecturer at JTMI UGM since 2002
• Educational Background:• Bachelor in Electrical Engineering (1995-1999)
Gadjah Mada University, Indonesia
• Magister of Management (1999-2001) Gadjah MadaUniversity, Indonesia
• International Master Program on Quality, Safety and
Environment (2006-2007), Otto von Guerricke University ofMagdeburg, Germany
• PhD in Industrial & Engineering Sciences (2008-2013),Swinburne University and Technology, Australia
• Research interest:
System Engineering, Operations Research, Tribology in railways
Who Am I
8/10/2019 Introduction System Modeling
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Basic modeling Mathematical modeling: overview Mathematical modeling: deterministic
Deterministic – static : LP, NLP, IP Deterministic – dynamic
Mathematical modeling: stochastic Parameter estimation
Verification and validation
Course Materials
• Williams, H.P., 1999, Model Building in MathematicalProgramming, John Wiley & Sons Ltd
• Murthy, D.N.P, Page, N.W, and Rodin, E.Y. (1990). Mathematical Modelling, Pergamon Press, Oxford.
• Law, A.M. and Kelton, D.W., 2000, Simulation Modelingand Analysis, 3rd ed., McGraw-Hill, New York.
• INCOSE, 2010, System Engineering Handbook
• Other sources
Course Materials
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Evaluation
No. Components Weight, %
1. Group assignment 202. Individual assignment 20 3. Mid Exam 304. Final Exam (compulsory ) 30
GRADE
85 – 100 A
75 ≤ X < 85 B65 ≤ X < 75 C
50 ≤ X < 65 D< 50 E
What is a system ?
An interconnected set of elements that iscoherently organized in a way thatachieves something (Donella H. Meadows,
2008)
A collection of components whereinindividual components are constrained byconnecting interrelationships such that
that system as a whole fulfills come specificfunctions in response to varying demands(IJ Nagrath & M. Gopal, 1990)
A group of interacting, interrelated, orinterdependent elements forming acomplex whole (Dell Zhang, Univ. ofLondon)
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Consists of objects called ENTITIESthat have a set of properties called ATTRIBUTES
Attributes can have forms of either VARIABLES (objects interactions) orPARAMETERS (intrinsic attributes)
Interactions between objects explainthe STATE and BEHAVIOUR ofsystem which are important in
achieving the PURPOSE/FUNCTION
System Components
ELEMENTS
INTER-CONNECTIONS
FUNCTION /PURPOSE
System Components
THINK ABOUT THIS:
Can you identify parts?
Pitfalls : no end identificationprocess due to many sub-elements:lose sight of the system, e.g. can’t seethe forest for the trees
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System Components
THINK ABOUT THIS:
Do the parts affect each other?
Do the parts together produce aneffect that is different from the effectof each part on its own?
1 + 1 = 2 ?OR
1 + 1 > 2 ?OR
1 + 1 < 2 ?It’s easier to learn system elements than about its
interconnections
System ComponentsTHINK ABOUT THIS:
Does the effect, the behavior over timepersist in a variety of circumstances?
At a time, if a frog turns right and catches a fly,and then turns left and catches a fly, and then
turns backward and catches a fly…
THE PURPOSE OF THE FROG ?
Turns right, turns left and the turns backwards ?
Another time, turn left, backward and then right Catching flies
Purpose are deduced from BEHAVIOR, not fromrhetoric or stated goals
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‘Everything should be made as simple as possible,
but not simpler.’ (Albert Einstein)
It is small,long and
moving, like asnake
It is a large, roughthing, wide andbroad like a rug
It is mightyand firm like
a pillar
System Environment
What the system does
SYSTEM ENVIRONMENT
SYSTEM BOUNDARY
How the systemis controlled
Inputs/excitations
Outputs /response
Feedback Feed-forward
Control
CAUSE VARIABLES: e.g. position of accelerator, brake pedal, gear level,steering wheel, the slope of highway (automobile driving system)
EFFECT VARIABLES: e.g. speed of automobile, the position ofautomobile on the highway (automobile driving system)
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Model
to describe
to explain
to predict the characteristics /structures and/or behavior of a
system (natural or man-made)
REPRESENT / APPROXIMATE the REAL WORLD
• Abstraction
• Simplification
Problem Situation
MODEL
IMPLEMENTASI
Performancemeasure
Design alternatives:
RepresentativenessUsefulnessUsabilityCost considerationTime frame
Model
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Have I solved this problem before? If so, do the same think again
Has someone else solved this problem? Look in textbooks, do a literature search, etc
Don’t waste time and money starting from scratch if
someone has already solved the problem unless youhave good reason to believe their model is notgood
Building ModelFirst question to ask ...
Understand the system and its characteristics
Set objective
Model formulation
Validate
Analysis Adequate? If not revise the model
Building ModelIf it’s a completely new problem...
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CREATIVITY
SKILL /
EXPERIENCES
THEORY
REAL
WORLD MODEL
SYSTEM
APPROACH
Building Model
what we need ...
The question that is being asked (the problemobjective)
The level of detail required
The resource available (time, personnel,computers, etc)
Type of model will depend on:
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System
Experiment withthe actual system
Experiment witha model of the
system
Physical modelMathematical
model
Analyt icalsolution
Simulation
Building Model
Basic Modelling
Identifikasi masalah
Karakterisasi sistem
Formulasi model (penentuan variabel dan parameter,estimasi parameter, etc.)
Validasi model konseptual
Design of experiments
Analisis
Validasi output
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System characterization
Open vs closed
White box vs black box
Static vs dynamic
Continuous vs discrete
Deterministic vs stochastic
Sistem terbuka jika objek di dalam sistem berinteraksi dengan objek di
luar sistem. Sebaliknya disebut sistem tertutup.
Thermal power plant
Sistem terbuka jika asal batubara dianggap objek di luar system yang
mempengaruhi sistem. Jaringan PLN dianggap objek lain yg dipengaruhi oleh
sistem
SistemTambang
batubaraJaringan PLN
Permintaan Soft drink
Jika satu-satunya variabel yaitu permintaan ke depan hanya dikaitkan dengan
permintaan yg lalu, sistem menjadi tertutup. Jika dikaitkan dengan perubahan
populasi, cuaca dan promosi, sistem terbuka.
Sistem
Populasi
Cuaca
Promosi
Permintaan soft drink
Open vs closed
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How much a prior i information on the system is available
Sistem terbuka tetapi struktur dalam sistem tersebut tidak diketahui, maka
deskripsi ini disebut black box (no a priori information)
estimate the functions “probably” could be adequate. Use
functions as general as possible to cover all different models.
Sebaliknya jika dapat digambarkan objek-objek di dalam sistem dan atribute-
atributnya disebut deskripsi white box (all necessary information is available).
if we use the information correctly, the model will behave correctly
complexity ↑
Medicine in human system
Usually the amount of medicine in the blood is an exponentially decaying
function. However, how rapidly does the medicine amount decay and what is
the initial amount of medicine in blood are unknown. These parameters have
to be estimated through some means before one can use the model
White box vs Black box
Jika waktu tidak berperan sehingga semua variabel juga independen
terhadap waktu, maka sistem adalah statik.
Sebaliknya jika waktu berperan sehingga variabel nilainya berubah dg waktu,
maka kita mempunyai sistem dinamik.
Alloy Selection
Jika problem ini digambarkan sebagai sistem lup tertutup dg 3 variabel yaitu A
koeffisien thermal, B metoda produksi dan C suplier
C
A
B
Rocket launch
Posisi dan kecepatan roket terhadap tempat peluncuran di bumi adalah berubah
dengan waktu. Hubungan antara posisi dan kecepatan dijelaskan dengan teori
dinamika.
Static vs Dynamic
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Jika variabel dalam sistem perlu digambarkan pada “all time instants”
(Continuous) atau hanya pada “relevant time instants” (discrete)Memilih continuous atau discrete tergantung banyak aspek dalam
pemodelan.
Jika “continuous” terlalu detail, bisa digunakan skala waktu “discrete”
Permintaan soft drink
Jika tertarik pada interval permintaan mingguan, maka varibel yang
menggambarkan sistem berubah dalam periode mingguan. Unsur waktu
diperlakukan sebagai discrete.
Polusi SungaiLevel konsentrasi zat pencemar di sungai pada lokasi tertentu berubah
secara kontinyu dengan waktu, sehingga digunakan pendekatan
continuous.
Continuous vs Discrete
• Deterministik: Jika nilai variabel (sistem statik) atau perubahan nilainya
(sistem dinamik) bersifat predictable dengan kepastian.
•Stokastik: Jika nilai atau perubahan nilai variabelnya random dan
unpredictable.
Keandalan komponen
Data waktu kegagalan komponen sebuah mesin menunjukkan adanya
variabilitas yang besar (37 s/d 415 jam) sehingga sistem tersebut
stokastik
Peluncuran Roket
Posisi dan kecepatan roket dapat diformulasikan secara akurat dari
teori dinamika sistem, sehingga posisi dan kecepatan roket dapat
diprediksi dengan akurasi yg tinggi pula. Sistem ini dipandang sebagai
deterministik.
Deterministic vs Stochastic