MODEL
&
MATHEMATICS
Disarikan oleh:
Prof Dr Ir Soemarno MS
WHAT IS SYSTEM MODELLING ?
Worthwhile
Recognition
Problems
Amenable
Compromise
Complexity
Definitions
Simplification
Bounding
Objectives
Hierarchy
Identification
Priorities
Goals
Generality
Solution
Family
Generation
Modelling
Evaluation
Implementation
Selection
Inter-relationship
Feed-back
Stopping rules
Sensitivity & Assumptions
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
MODEL & MATEMATIK: Term
Variabel
Parameter
Tipe
Konstante
Likelihood
Dependent
Populasi
Probability
Analitik
Independent
Maximum
Sampel
Regressor
Simulasi
MODEL & MATEMATIK: Definition
Preliminary
Formal
Expression
Words
Mathematical
Goodall
Mapping
Rules
Representational
Maynard-Smith
Predicted
values
Homomorph
Model
Physical
Mathematical
Comparison
Symbolic
Simplified
Data values
Simulation
MODEL & MATEMATIK: Relatives
Advantages
Disadvantages
Distortion
Precise
Abstract
Transfer
Opaqueness
Complexity
Replacement
Communication
MODEL & MATEMATIK: Families
Types
Dynamics
Compartment
Stochastic
Multivariate
Network
Basis
Choices
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.
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.
DYNAMIC MODEL
MODELLING
SIMULATION
Dynamics
Equations
Computer
FORMAL
Language
ANALYSIS
Special
DYNAMO
CSMP
CSSL
General
BASIC
DYNAMIC MODEL
DIAGRAMS
SYMBOLS
RELATIONAL
LEVELS
AUXILIARY
VARIABLES
RATE
EQUATIONS
PARAMETER
SINK
MATERIAL
FLOW
INFORMATION
FLOW
DYNAMIC MODEL:
ORIGINS
Abstraction
Computers
Equations
Steps
Hypothesis
Discriminant
Function
Simulation
Other
functions
Exponentials
Logistic
Undestanding
MATRIX MODEL
MATHEMATICS
Operations
Additions
Substraction
Multiplication
Inversion
Matrices
Eigen value
Elements
Dominant
Types
Eigen vector
Square
Rectangular
Diagonal
Identity
Vectors
Row
Column
Scalars
MATRIX MODEL
DEVELOPMENT
Interactions
Groups
Materials
cycles
Size
Development
stages
Stochastic
Markov
Models
STOCHASTIC MODEL
STOCHASTIC
Probabilities
History
Statistical
method
Other Models
Dynamics
Stability
STOCHASTIC MODEL
Spatial patern
Distribution
Pisson
Example
Poisson
Negative
Binomial
Binomial
Negative
Binomial
Others
Test
Fitting
STOCHASTIC MODEL
ADDITIVE MODELS
Basic Model
Example
Error
Estimates
Analysis
Parameter
Variance
Orthogonal
Block
Effects
Experimental
Treatments
Significance
STOCHASTIC MODEL
REGRESSION
Model
Example
Error
Linear/ Nonlinear functions
Decomposition
Equation
Theoritical
base
Oxygen uptake
Reactions
Experimental
Assumptions
Empirical base
STOCHASTIC MODEL
MARKOV
Analysis
Example
Assumptions
Analysis
Transition
probabilities
Raised mire
Disadvantage
Advantages
MULTIVARIATE MODELS
METHODS
VARIATE
Variable
Classification
Dependent
Independent
Descriptive
Principal
Component
Analysis
Predictive
Discriminant
Analysis
Cluster
Analysis
Reciprocal
averaging
Canonical
Analysis
MULTIVARIATE MODEL
PRINCIPLE COMPONENT ANALYSIS
Requirement
Example
Environment
Organism
Regions
Correlation
Eigenvalues
Objectives
Eigenvectors
MULTIVARIATE MODEL
CLUSTER ANALYSIS
Example
Spanning tree
Multivariate
space
Demography
Rainfall
regimes
Minimum
Similarity
Single linkage
Distance
Settlement
patern
MULTIVARIATE MODEL
CANONICAL CORRELATION
Example
Correlation
Partitioned
Watershed
Urban area
Eigenvalues
Irrigation
regions
Eigenvectors
MULTIVARIATE MODEL
Discriminant function
Example
Discriminant
Calculation
Villages
Vehicles
Test
Structures
OPTIMIZATION MODEL
OPTIMIZATION
Dynamic
Meanings
Indirect
Simulation
Minimization
Experimentation
NonLinear
Linear
Objective function
Constraints
Solution
Examples
Maximization
Optimum Transportation Routes
Optimum irrigation scheme
Optimum Regional Spacing
MODELLING PROCESS
System analysis
Introduction
Processes
Model
Bounding
Systems
Definition
Word Models
Impacts
Factorial
Confounding
Alternatives
Separate
Combinations
Hypotheses
Data
Modelling
Analysis
Choices
Validation
Plotting
Outliers
Test
Estimates
Conclusion
Integration
Space
Time
Niche
Elements
Communication
MODELLING PROCESSES
HYPOTHESES
Decision Table
Relevance
Variable
Processes
Linkages
Impacts
Relationships
Linear
Non-Linear
Species
Interactive
Sub-systems
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
Subjectives
Sensitivity
Analysis
Uncertainty
Analysis
Resources
Objectivities
Experiments
Reasonableness
Interactions
ROLE OF THE COMPUTER
Roles
Introduction
Reasons
Speed
Data
Algoritm
Comparison
Speed
Implication
Techniques
Errors
Plotting
Waste
Program
High level
Language
Information
FORTRAN
BASIC
ALGOL
Machine code
Special
Development
Conclusions
Repetition
Checking
9/10
Modelling
Data
Algoritms
Manual
Calculator
Computer
Programming
DYNAMO.
Etc.
ROLE OF THE COMPUTER
DATA
Machine readable
Cautions
Availability
Sampling
Format
Punched card
Exchange
Paper tape
Format
Reanalysis
Magnetic
Tape
Data banks
Disc
MODEL
&
MATHEMATICS