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MODEL & MATHEMATICS DR. HERI NUGRAHA. SE. MSi. WHAT IS SYSTEM MODELLING ?. Worthwhile. Recognition. Problems . Amenable. Compromise. Complexity. Definitions. Simplification. Bounding. Objectives. Hierarchy. Identification . Priorities. Goals. Generality. Solution. Family.

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slide1
MODEL

&

MATHEMATICS

DR. HERI NUGRAHA. SE. MSi

slide2
WHAT IS SYSTEM MODELLING ?

Worthwhile

Recognition

Problems

Amenable

Compromise

Complexity

Definitions

Simplification

Bounding

Objectives

Hierarchy

Identification

Priorities

Goals

Generality

Solution

Family

Generation

Selection

Modelling

Inter-relationship

Feed-back

Stopping rules

Evaluation

Sensitivity & Assumptions

Implementation

slide3
PHASES OF SYSTEM MODELLING

Recognition

Definition and bounding of the problems

Identification of goals and objectives

Generation of solution

MODELLING

Evaluation of potential courses of action

Implementation of results

slide4
MODEL & MATEMATIK: Term

Tipe

Konstante

Variabel

Parameter

Likelihood

Dependent

Populasi

Probability

Analitik

Independent

Maximum

Sampel

Simulasi

Regressor

slide5
MODEL & MATEMATIK: Definition

Preliminary

Mathematical

Goodall

Mapping

Rules

Formal Expression

Representational

Maynard-Smith

Predicted values

Words

Homomorph

Model

Comparison

Physical

Symbolic

Data values

Simulation

Mathematical

Simplified

slide6
MODEL & MATEMATIK: Relatives

Disadvantages

Advantages

Distortion

Precise

Opaqueness

Abstract

Complexity

Transfer

Replacement

Communication

slide7
MODEL & MATEMATIK: Families

Basis

Choices

Types

Dynamics

Compartment

Stochastic

Multivariate

Network

slide8
BEBERAPA PENGERTIAN

MODEL DETERMINISTIK: Nilai-nilai yang diramal (diestimasi, diduga) dapat dihitung secara eksak.

MODEL STOKASTIK: Model-model yang diramal (diestimasi, diduga) tergantung pada distribusi peluang

POPULASI: Keseluruhan individu-individu (atau area, unit, lokasi dll.) yang diteliti untuk mendapatkan kesimpulan.

SAMPEL: sejumlah tertentu individu yang diambil dari POPULASI dan dianggap nilai-nilai yang dihitung dari sampel dapat mewakili populasi secara keseluruhan

PARAMETER: Nilai-nilai karakteristik dari populasi

KONSTANTE, KOEFISIEAN: nilai-nilai karakteristik yang dihitung dari SAMPEL

VARIABEL DEPENDENT: Variabel yang diharapkan berubah nilainya disebabkan oleh adanya perubahan nilai dari variabel lain

VARIABEL INDEPENDENT: variabel yang dapat menyebabkan terjadinya perubahan VARIABEL DEPENDENT.

slide9
BEBERAPA PENGERTIAN

MODEL FITTING: Proses pemilihan parameter (konstante dan/atau koefisien yang dapat menghasilkan nilai-nilai ramalan paling mendekati nilai-nilai sesungguhnya

ANALYTICAL MODEL: Model yang formula-formulanya secara eksplisit diturunkan untuk mendapatkan nilai-nilai ramalan, contohnya: MODEL REGRESI

MODEL MULTIVARIATE

EXPERIMENTAL DESIGN

STANDARD DISTRIBUTION, etc

SIMULATION MODEL: Model yang formula-formulanya diturunkan dengan serangkaian operasi arithmatik, misal:

Solusi persamaan diferensial

Aplikasi matrix

Penggunaan bilangan acak, dll.

slide10
DYNAMIC MODEL

MODELLING

SIMULATION

Equations

Dynamics

Computer

FORMAL

Language

ANALYSIS

Special

General

DYNAMO

CSMP

CSSL

BASIC

slide11
DYNAMIC MODEL

DIAGRAMS

SYMBOLS

RELATIONAL

AUXILIARY VARIABLES

LEVELS

MATERIAL FLOW

RATE EQUATIONS

PARAMETER

INFORMATION FLOW

SINK

slide12
DYNAMIC MODEL:

ORIGINS

Abstraction

Equations

Steps

Computers

Hypothesis

Discriminant Function

Simulation

Other functions

Undestanding

Logistic

Exponentials

slide13
MATRIX MODEL

MATHEMATICS

Matrices

Eigen value

Operations

Elements

Dominant

Additions

Substraction

Multiplication

Inversion

Types

Eigen vector

Square

Rectangular

Diagonal Identity

Vectors

Scalars

Row

Column

slide14
MATRIX MODEL

DEVELOPMENT

Interactions

Groups

Stochastic

Materials cycles

Size

Markov Models

Development stages

slide15
STOCHASTIC MODEL

STOCHASTIC

Probabilities

History

Other Models

Statistical method

Dynamics

Stability

slide16
STOCHASTIC MODEL

Spatial patern

Distribution

Example

Pisson

Poisson

Negative Binomial

Binomial

Negative Binomial

Fitting

Test

Others

slide17
STOCHASTIC MODEL

ADDITIVE MODELS

Basic Model

Example

Error

Estimates

Analysis

Parameter

Variance

Orthogonal

Block

Effects

Experimental

Significance

Treatments

slide18
STOCHASTIC MODEL

REGRESSION

Model

Example

Error

Decomposition

Equation

Linear/ Non-linear functions

Theoritical base

Oxygen uptake

Reactions

Experimental

Empirical base

Assumptions

slide19
STOCHASTIC MODEL

MARKOV

Analysis

Example

Assumptions

Analysis

Disadvantage

Advantages

Transition probabilities

Raised mire

slide20
MULTIVARIATE MODELS

METHODS

VARIATE

Variable

Classification

Dependent

Descriptive

Predictive

Principal Component Analysis

Discriminant Analysis

Independent

Cluster Analysis

Reciprocal averaging

Canonical Analysis

slide21
MULTIVARIATE MODEL

PRINCIPLE COMPONENT ANALYSIS

Requirement

Example

Correlation

Objectives

Environment

Eigenvalues

Eigenvectors

Organism

Regions

slide22
MULTIVARIATE MODEL

CLUSTER ANALYSIS

Example

Spanning tree

Multivariate space

Demography

Rainfall regimes

Minimum

Similarity

Single linkage

Distance

Settlement patern

slide23
MULTIVARIATE MODEL

CANONICAL CORRELATION

Example

Correlation

Partitioned

Watershed

Urban area

Eigenvalues

Eigenvectors

Irrigation regions

slide24
MULTIVARIATE MODEL

Discriminant function

Example

Discriminant

Calculation

Villages

Vehicles

Test

Structures

slide25
OPTIMIZATION MODEL

OPTIMIZATION

Dynamic

Meanings

Indirect

Non-Linear

Linear

Simulation

Objective function

Minimization

Constraints

Experimentation

Solution

Examples

Maximization

Optimum Transportation Routes

Optimum irrigation scheme

Optimum Regional Spacing

slide26
MODELLING PROCESS

System analysis

Introduction

Processes

Model

Space

Time

Niche

Elements

Bounding

Systems

Definition

Word Models

Impacts

Factorial

Confounding

Alternatives

Separate

Combinations

Hypotheses

Data

Plotting

Outliers

Modelling

Analysis

Test

Choices

Estimates

Validation

Conclusion

Integration

Communication

slide27
MODELLING PROCESSES

HYPOTHESES

Decision Table

Relevance

Processes

Relationships

Variable

Linkages

Linear

Impacts

Non-Linear

Species

Interactive

Sub-systems

slide28
HYPOTHESES

Hypotheses of Relevance: Mengidentifikasi dan mendefinisikan variabel dan subsistem yang relevan dengan permasalahan yang diteliti

Hypotheses of Processes: Menghubungkan subsistem (atau variabel) di dalam permasalahan yang diteliti dan mendefinisikan dampak (pengaruh) terhadap sistem yang diteliti

Hypotheses of relationships: Merumuskan hubungan-hubungan antar variabel dengan menggunakan formula-formula matematik (fungsi linear, non-linear, interaksi, dll)

slide29
MODELLING PROCESSES

VALIDATION

Verification

Critical Test

Sensitivity Analysis

Subjectives

Uncertainty

Analysis

Resources

Objectivities

Experiments

Interactions

Reasonableness

slide30
ROLE OF THE COMPUTER

Roles

Speed

Data

Algoritm

Introduction

Reasons

Manual

Calculator

Computer

Comparison

Speed

Techniques

Errors

Plotting

Implication

Repetition

Checking

Waste

9/10

Modelling

Data

FORTRAN

BASIC

ALGOL

Program

High level

Algoritms

Language

Machine code

DYNAMO. Etc.

Special

Information

Development

Conclusions

Programming

slide31
ROLE OF THE COMPUTER

DATA

Machine readable

Cautions

Availability

Format

Sampling

Punched card

Exchange

Paper tape

Format

Reanalysis

Magnetic

Tape

Data banks

Disc

slide32
MODEL

&

MATHEMATICS

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