introduction system modeling

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



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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

introduction system modeling

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