MODEL &

MATHEMATICS

Disarikan oleh:Prof Dr Ir Soemarno MS

WHAT IS SYSTEM MODELLING ?

Recognition

Definitions

Problems

Evaluation

Identification

Feed-back

Solution

Modelling

Amenable

Worthwhile

Compromise

Bounding

Complexity

Simplification

Stopping rules

Generality

GenerationFamily

Selection

Objectives Hierarchy

PrioritiesGoals

Inter-relationship

Sensitivity & Assumptions Implementation

PHASES OF SYSTEM MODELLING

Recognition

Definition and bounding of the problems

Generation of solution

Identification of goals and objectives

MODELLING

Evaluation of potential courses of action

Implementation of results

MODEL & MATEMATIK: Term

Variabel ParameterLikelihood

Konstante Tipe

Dependent

Independent

Regressor

Populasi

Sampel

Probability

Maximum

Analitik

Simulasi

MODEL & MATEMATIK: Definition

Preliminary Goodall Mathematical

Formal Expression

Words

Physical

Mapping

Representational

Rules

Predicted values

Maynard-Smith

Comparison

Mathematical

Homomorph

Symbolic

Simplified Data values

Model

Simulation

MODEL & MATEMATIK: Relatives

Advantages Disadvantages

Precise

Abstract

Communication

Distortion

Opaqueness

Transfer Complexity

Replacement

MODEL & MATEMATIK: Families

Types Basis

Dynamics

Compartment

Network

Choices

Stochastic

Multivariate

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

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.

PARAMETER: Nilai-nilai karakteristik dari populasi

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

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 MULTIVARIATEEXPERIMENTAL DESIGNSTANDARD DISTRIBUTION, etc

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

Solusi persamaan diferensialAplikasi matrixPenggunaan bilangan acak, dll.

DYNAMIC MODEL

MODELLING

Dynamics SIMULATION

Language

Equations

Computer

GeneralSpecial

DYNAMOCSMPCSSL

BASIC

FORMAL

ANALYSIS

DYNAMIC MODEL

DIAGRAMS

RELATIONAL SYMBOLS

RATE EQUATIONS

LEVELS

PARAMETER

INFORMATION FLOWSINK

AUXILIARY VARIABLES MATERIAL

FLOW

DYNAMIC MODEL:

ORIGINS

Computers Equations

Other functions

Steps

Discriminant Function

Undestanding

Simulation

Abstraction

Hypothesis

LogisticExponentials

MATRIX MODEL

MATHEMATICS

Operations Matrices

Types

Eigen value

Elements

SquareRectangular

Diagonal Identity Vectors

Dominant

Eigen vector

Scalars

RowColumn

AdditionsSubstraction

MultiplicationInversion

MATRIX MODEL

DEVELOPMENT

Interactions Groups

Development stages

Stochastic

Size Materials

cycles Markov Models

STOCHASTIC MODEL

STOCHASTIC

Probabilities History

Stability

Other Models

Statistical method Dynamics

STOCHASTIC MODEL

Spatial patern

Distribution Example

Binomial

Pisson Poisson

Negative Binomial

Others

Negative Binomial

Fitting Test

STOCHASTIC MODEL

ADDITIVE MODELS

Basic Model Example

Parameter

Error Estimates

Block

Treatments

Analysis

Effects

Orthogonal

Experimental Significance

Variance

STOCHASTIC MODEL

REGRESSION

Model Example

Linear/ Non-linear functions

Error Decomposition

Assumptions

Equation

Reactions

Oxygen uptake

Experimental Empirical base

Theoritical base

STOCHASTIC MODEL

MARKOV

Example Assumptions

Transition probabilities

Analysis Disadvantage

Raised mire

Advantages

Analysis

MULTIVARIATE MODELS

METHODS

Variable Classification

Independent

Dependent Descriptive Predictive

VARIATE

Principal Component

Analysis

Cluster Analysis

Reciprocal averaging

Canonical Analysis

Discriminant Analysis

MULTIVARIATE MODEL

PRINCIPLE COMPONENT ANALYSIS

Example Correlation

Organism

Environment Eigenvalues

Regions

Objectives

Requirement

Eigenvectors

MULTIVARIATE MODEL

CLUSTER ANALYSIS

Example Spanning tree

Rainfall regimes

Demography

Minimum

Settlement patern

Multivariate space

Similarity

Distance

Single linkage

MULTIVARIATE MODEL

CANONICAL CORRELATION

Example Correlation

Urban area

WatershedPartitioned

Irrigation regions

Eigenvalues Eigenvectors

MULTIVARIATE MODEL

Discriminant function

Example Discriminant

Vehicles

VillagesCalculation

Structures

Test

OPTIMIZATION MODEL

OPTIMIZATION

Meanings Indirect

Minimization

Simulation Objective function

Maximization

Linear

Experimentation

Constraints

Solution

Examples

Non-Linear

Dynamic

Optimum Transportation RoutesOptimum irrigation schemeOptimum Regional Spacing

MODELLING PROCESS

Introduction

Definition

System analysis

Integration

Hypotheses

Conclusion

Modelling

Validation

ModelProcesses

Bounding

Word Models

Alternatives

Systems

Impacts

SpaceTimeNiche

Elements

FactorialConfounding

SeparateCombinations

Communication

Data

Analysis

Choices

Test

Estimates

PlottingOutliers

MODELLING PROCESSES

HYPOTHESES

Relevance Processes

Species

Variable Linkages

Sub-systems

Relationships

Decision Table

Impacts

Interactive

Linear

Non-Linear

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)

MODELLING PROCESSES

VALIDATION

Verification Critical Test

Objectivities

Subjectives

Experiments

Reasonableness

Sensitivity Analysis

Analysis

Interactions

Uncertainty

Resources

ROLE OF THE COMPUTER

Introduction

Speed

Roles

Conclusions

Data

Development

Algoritms

Reasons

SpeedData

Algoritm

Comparison

Implication

Waste

TechniquesErrors

Plotting

ManualCalculatorComputer

RepetitionChecking

9/10Modelling

Programming

Program

Language

Information

High level

Special

Machine code

FORTRANBASIC

ALGOL

DYNAMO. Etc.

ROLE OF THE COMPUTER

DATA

Cautions Availability

Format

Sampling

Reanalysis

Data banks

Format

Exchange

Magnetic

Punched card

Paper tape

Machine readable

Tape

Disc

MODEL

&

MATHEMATICS