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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. - PowerPoint PPT Presentation
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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