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Pertemuan 22 MODEL SIMULASI. Matakuliah: D0174/ Pemodelan Sistem dan Simulasi Tahun: Tahun 2009. Learning Objectives. Konsep Model Konsep Simulasi Model Simulasi Trade Off Simulasi. Modeling Throughout System Develompent.

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Pertemuan 22 MODEL SIMULASI

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## Pertemuan 22MODEL SIMULASI

Matakuliah: D0174/ Pemodelan Sistem dan Simulasi

Tahun: Tahun 2009

### Learning Objectives

• Konsep Model

• Konsep Simulasi

• Model Simulasi

### Modeling Throughout System Develompent

• The purpose is to provide a more organized and expanded picture of the use of modeling tools in support of systems engineering decision making and related activities.

• The goal is to provide an awareness of the importance of modeling to the successful practice of system engineering.

### System Engineering Decision Tools is organized intro 3 sections :

A. Modeling

describes a number of the most commonly used static representation employed in system development.

B. Simulation

discusses several types of dynamic system representations used in various stages of system development.

analysis describes the modeling approach to the analysis of the alternatives.

### A. Modeling

Modeling guides decisions in the face of complexity and uncertainty :

• Modeling illuminates the behavior and relationship of key issues.

• Simulation is the modeling of dynamic behavior.

• Trade-off analysis models the decision process among alternative choices.

### Types of Models

1. Schematic models, which use diagrams to represent system elements or processes.

2. Mathematical models, which use mathematical notation to represent relationships.

3. Physical models, which are physical representations of system or system elements.

### 1. Schematic Models

• Several types of schematic models :

• Cartoons

• Architectural Models

• System Block Diagrams

• System Context Diagrams

• Functional Flow Block Diagrams

• Data Flow Diagrams (DFD)

• IDEF0 Diagrams

• Functional Flow Process Diagrams

### Schematic Models

• Trigonal System Models

• Unified Modeling Language

Examples of schematic models

• An architect’s sketches.

• Floor layouts.

• ### System Block Diagrams

• System block diagrams model system organization :

• They are often arranged in a tree-like structure to represent hierarchical organizations

• Simple rectangular boxes represent physical or other elements

### System Context Diagrams

• System context diagrams show all external entities that interact with the system, where :

• The system is represented as a “black box” (not showing internal structure)

• The diagrams describe the system’s interactions with its environment

### Functional Flow Block Diagrams (FFBD)

• Functional flow block diagrams model functional interactions, where :

• Functional elements are represented by rectangle

• Interactions show flow of information, material, or energy between elements

• The names of the elements begin with a verb, denoting action

• Connecting lines are labeled with the names of the flows

• Examples and extensions FFBDs include :

-System life cycle models in the text

-IDEF0 diagrams

-Functional flow diagrams and descriptions

### Functional Flow Process Diagrams (FFPD)

• Functional flow process diagrams model processes and :

• Form a hierarchical description of a complex process

• Interrelate process design with requirements and specifications

• Are similar to how FFBDs model systems

### Trigonal System Models

• Trigonal system models decompose complex systems into :

• Input

• Processing

• Output

• Each of these can usually themselves be decomposed into their input, processing, and output functions

### Unified Modeling Language (UML)

• Uses nine models to represent an object-oriented software system or element

• Is widely used in software development

• Is supported by a number of commercial modeling tools

### 2. Mathematical Models

• Several types of mathematical models :

• Approximate Calculations

• Elementary Relationships

• Statistical Distributions

• Graphs

• Mathematical models are important aids to system developments, because :

• They are useful both for design and systems engineering

• They can perform “sanity checks” on results of complex analyses and simulations

### 3. Physical Models

• Several types of physical models :

• Scale models

• Mock-ups

• Prototypes

• Physical models are extensively used in system design and testing, and include :

• Test models

• Mock ups

• Prototypes

### B. Types of Simulation

Operational Simulation

War Games

System Effectiveness Simulation

Mission Simulation

Physical Simulation

Hardware-in-the-loop Simulation

Engineering Simulation

Environmental Simulation

Virtual Reality Simulation

Development of System Simulations

Simulation Verification and Validation

### Types of Simulation

1. Environmental Simulation

• Types of environmental simulation :

• Mechanical Stress Testing

• Crash Testing

• Wind Tunnel Testing

• Subject systems and system elements to stressful conditions

• Generate synthetic system environments

• Test systems’ conformance to operational requirements

### Types of Simulation

2. System Simulation

• System simulations deal with the dynamic behavior of systems and system elements and :

• Used in every phase of system development

• Management of simulation effort is a systems engineering responsibility

Example Of Operational Simulations

• One of the is Computer “War Games”, which :

• Involve a simulated adversarial system operated by two teams of players

• Used to asses the operational effectiveness of tactics and system variants

### Types of Simulation

3, System Effectiveness Simulation

• System effectiveness simulation assess alternative system architectures and “

• Used during conceptual development to make comparative evaluations

• The design of effectiveness simulations is itself a complex systems engineering task.

4. Developing Complex Simulation

• Developing complex simulation must seek a balance between fidelity and cost :

• Such simulations can be systems in their own right

• Socpe must be controlled to obtain effective and timely results

### Types of Simulation

5. Physical Simulations

• Used in the design of high-performance vehicles and other dynamic systems

• Can save enormous amounts of development time and cost

6. Hardware-in-the-loop Simulations

• Include hardware components coupled to computer-driven mechanisms

• A form of physical simulation, modeling dynamic operational environments

### Types of Simulation

7. Virtual Reality Simulation

• Types of virtual reality simulation :

• Spatial Simulation

• Video Games

• Battlefield Simulation

• Trade-offs are aids to decision making if :

• They are not infallible formulae for success

• Numerical results produce an exaggerated impression of the accuracy credibility

• The apparent winner is not decisively superior further analysis is necessary

• A trade-off, formal or informal, consists of the following steps :

• Define the objective

• Identify qualified alternative candidates

• Define measures of effectiveness (MOE) and their relative importance

• Evaluate each alternative with respect to each MOE

• Combine the evaluations for each alternative

• Select the best overall performing alternative

• Analyze the basis and robustness of the results

• Involved consciously or subconsciously in every decision

• Stimulate consideration of alternatives

• Select the “best” course of action from two or more alternatives

Major decisions require formal trade-off analysis.

### Model Simulasi Kontinu

• Definisi “Merupakan model yang berfokus pada struktur dan perilaku sistem yang terdiri dari interaksi antar variabel dan umpan balik.

• Macam umpan balik ;

1. Umpan balik positif.

2. Umpan balik negatif.

### Ventana Simulation (VENSIM)

• Definisi “Ventana simulation adalah bahasa simulasi yang dapat digunakan sebagai alat untuk membantu menyelesaikan masalah-masalah bisnis maupun teknis.“(Software)

• Persamaan dalam Vesin ;

1. Level, persamaan dimana proses akumulasi dihitung.

2. Inisialisasi, level memerlukan nilai awal.

3. Rate, persamaan rate baru dipakai untuk nilai aliran masuk dan aliran keluar dari sebuah level.

4. Auxiliary, variabel dinamis yang dihitung dari variabel lain dalam waktu tertentu.

5. Konstanta, nilai yang selalu tetap.

Fungsi-fungsi dalam Vensim ;

ABS (x) menghasilkan nilai absolute dari x.

ACTIVE_INITIAL, menghasilkan persamaan aktif sepanjang periode simulasi, kecuali jika diperlukan untuk menentukan nialai awal.

ALLOC_P, menghasilkan sejumlah permintaan yang dialokasikan atas permintaan dan prioritas tertentu.

CUMULATE (X), mengambil input data x kemudian menghasilkan kumulasi data tersebut.

DELAY_FIXED, input, waktu delay, nilai awal. Menghasilkan nilai input yang tertunda selama waktu delay. Nilai awal adalah nilai variabel di sisi kiri persamaan pada awal dimulainya simulasi. Waktu delay dapat berupa ekspresi.

FORECAST, input, waktu rata-rata, horizon,menghasilkan suatu peramalan atas nilai input untuk selang waktu horizon. Fungsi ini dapat meramalkan tren ekstrapolasi sederhana untuk menghasilkan nilai variabel di masa mendatang berdasarkan nilai-nilai yang sebelumnya.

GAME (X), menghasilkan nilai x sepanjang periode simulasi.

IF_THEN_ELSE, kondisi, nilai benar, nilai salah, menghasilkan nilai benar jika kondisi bernilai benar, nilai salah jika jika kondisi benar salah. Kondisi haruslah berupa persamaan Boolean atau sebuah eksresi atau sebuah variabel yang dapat diinterprestasikan sebagai sebuah nilai Boolean.

INITIAL (A), menghasilkan nilai A pada awal simulasi dan bersifat tetap sepanjang periode simulasi. Fungsi ini digunakan untuk mencatat nilai awal sebuah variabel.

INTEG, rate, nilai awal, merupakan nilai integral dari rate secara numeric. Nilai awal adalah nilai variabel di sisi kiri persamaan pada awal simulasi.

INTEGER (X), menghasilkan nilai integer trbesat lebih kecil atau sama dengan X.

LOOKUP_AREA, lookup, awal, ahkir, menghasilkan area dibawah tabel look up diantara awal dan ahkir. Dapat digunakan untuk menormalisasi look up.

MARKET (permintaan[pertama], prioritas [pertama], ukuran, lebar, supply). Bila digunakan secara konjungtif dengan ALLOC_P, menghasilkan prioritas sedemikian hingga total alokasi atas sumber daya yang langka dapat dengan tepat memenuhi supply dari sumber daya tersebut.

MAX (A,B). Menghasilkan nilai tersebar antara A dan B.

MIN, (A,B). Menghasilkan nilai terbesar antara B dan A.

PULSE (awal, lebar). Menghasilkan 1.0 dimulai pada saat awal dan berlangsung selama selang interval.

QUANTUM (A,B) menghasilkan nilai bilangan terkecil atau sama dengan A yang merupakan integer kelipatan B. Kegunaan utama fungsi ini adalah untuk menghapus bagian non integer dari sebuah nilai.

RAMP (slop, waktu mulai, waktu akhir). Menghasilkan nilai 0 sampai dengan waktu mulai, lalu kemudian bertambah dengan kemiringan slope sampai waktu akhir, untuk kemudian menjadi konstan.

RANDOM_0_(). Fungsi ini berdistribusi seragam (uniform) dengan range dari 0 sampai dengan 1. User dapat mengganti dengan rentang yang lain secara bebas.

RANDOM_EXPONNTIAL(). Menghasilkan distribusi eksponensial dengan nilai mean = 1.

RANDOM_NORMAL(). Menghasilkan distribusi normal dengan mean = 1 dan variasi = 1.

• SAMPLE IF TRUE (kondisi, input, nilai awal). Menghasilkan nilai input jika kondisi bernilai benar, selain itu nilainya akan tetap. Pada awalnya nilai ini akan tetap pada nilai awal. Fungsi ini berguna untuk memperoleh informasi perihal perilaku variabel.

• SMOOTH (input, waktu delay). Menghasilkan sebuah permulusan eksponensial terhadap input.

• STEP (height, waktu step). Menghasilkan nilai nol sampai dengan waktu step, lalu menghasilkan height setelahnya.

• TIME_BASE (awal, slope). Menghasilkan basis waktu baru yang memiliki nilai awal ketika waktu adalah nol lalu meningkat dengan kemiringan slop relatif terhadap waktu.

• TREND (input, waktu rata-rata dan tren awal). Menghasilkan laju pertumbuhan pecahan rata-rata (pertumbuhan negatif) dalam input.

• XIDZ (A,B,X). Merupakan operasi penbagia A dengan B. Jika nilai B adalah 0, maka hasil perhitungan adalah X. XIDZ biasanya dipakai untuk mengungkapkan keterbatasan dari A/B jika B mendekati 0.

• ZIDZ (A,B). Membagi A dengan B jika B = 0, maka hasil perhitungan adalah nol. Biasanya digunakan untuk mengekspresikan kasus khusus dimana keterbatasan A/B adalah ketika B mendekati nol, hasilnya adalah nol.

• Fungsi Tabel dipakai dalam mempresentasikan hubungan non linier diantara variabel model apabila persamaan hubungan ini begitu rumit jika dituliskan secara matematis. Dalam Vesim, penulisan kooerdinat tabel dilakukan di pilihan “Graph Lookup” dipojok kanan atas window.

Contoh-contoh model dalam Ventana Simulation ;

• Model populasi.

• Model persediaan barang dan harga.

• Model jumlah order dalam proses.

• Membuat strip graph

### Daftar Pustaka

Harrel. Ghosh. Bowden. (2000). Simulation Using Promodel. McGraw-Hill. New York.

Alexander Karsiakoff. William N Sweet.(2003). System Engineering Principle & Practice. John Wiley & Sons. New Jersey.