MODEL & MATHEMATICS DR. HERI NUGRAHA. SE. MSi.

Presentasi berjudul: "MODEL & MATHEMATICS DR. HERI NUGRAHA. SE. MSi."— Transcript presentasi:

1 MODEL & MATHEMATICS DR. HERI NUGRAHA. SE. MSi

2 WHAT IS SYSTEM MODELLING ? Sensitivity & Assumptions
Worthwhile Recognition Problems Amenable Compromise Complexity Definitions Bounding Simplification Objectives Hierarchy Identification Priorities Goals Generality Solution Family Generation Selection Modelling Inter-relationship Feed-back Stopping rules Evaluation Sensitivity & Assumptions Implementation

3 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

4 MODEL & MATEMATIK: Term
Tipe Konstante Variabel Parameter Likelihood Dependent Populasi Probability Analitik Independent Maximum Sampel Simulasi Regressor

5 MODEL & MATEMATIK: Definition
Preliminary Goodall Mathematical Mapping Rules Formal Expression Representational Maynard-Smith Predicted values Words Homomorph Model Comparison Physical Symbolic Data values Mathematical Simulation Simplified

6 MODEL & MATEMATIK: Relatives
Disadvantages Advantages Distortion Precise Opaqueness Abstract Complexity Transfer Replacement Communication

7 MODEL & MATEMATIK: Families
Types Basis Choices Dynamics Compartment Stochastic Multivariate Network

8 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.

9 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.

10 DYNAMIC MODEL MODELLING Dynamics SIMULATION Equations Computer FORMAL
Language ANALYSIS Special General DYNAMO CSMP CSSL BASIC

11 DYNAMIC MODEL DIAGRAMS SYMBOLS RELATIONAL AUXILIARY VARIABLES LEVELS
MATERIAL FLOW RATE EQUATIONS PARAMETER INFORMATION FLOW SINK

12 Discriminant Function
DYNAMIC MODEL: ORIGINS Abstraction Computers Equations Steps Hypothesis Discriminant Function Simulation Other functions Undestanding Logistic Exponentials

13 MATRIX MODEL MATHEMATICS Operations Matrices Eigen value Elements
Dominant Additions Substraction Multiplication Inversion Types Eigen vector Square Rectangular Diagonal Identity Vectors Scalars Row Column

14 MATRIX MODEL DEVELOPMENT Interactions Groups Stochastic
Materials cycles Size Markov Models Development stages

15 STOCHASTIC MODEL STOCHASTIC Probabilities History Other Models
Statistical method Dynamics Stability

16 STOCHASTIC MODEL Spatial patern Distribution Example Pisson Poisson
Negative Binomial Binomial Negative Binomial Fitting Test Others

17 STOCHASTIC MODEL ADDITIVE MODELS Basic Model Example Error Estimates
Analysis Parameter Variance Orthogonal Block Effects Experimental Significance Treatments

18 Linear/ Non-linear functions
STOCHASTIC MODEL REGRESSION Model Example Error Decomposition Equation Linear/ Non-linear functions Theoritical base Oxygen uptake Reactions Experimental Empirical base Assumptions

19 Transition probabilities
STOCHASTIC MODEL MARKOV Analysis Example Assumptions Analysis Disadvantage Advantages Transition probabilities Raised mire

20 Principal Component Analysis Discriminant Analysis
MULTIVARIATE MODELS METHODS VARIATE Variable Classification Dependent Descriptive Predictive Principal Component Analysis Discriminant Analysis Independent Cluster Analysis Reciprocal averaging Canonical Analysis

21 PRINCIPLE COMPONENT ANALYSIS
MULTIVARIATE MODEL PRINCIPLE COMPONENT ANALYSIS Requirement Example Correlation Objectives Environment Eigenvalues Eigenvectors Organism Regions

22 MULTIVARIATE MODEL CLUSTER ANALYSIS Example Spanning tree
Multivariate space Demography Rainfall regimes Minimum Similarity Single linkage Distance Settlement patern

23 CANONICAL CORRELATION
MULTIVARIATE MODEL CANONICAL CORRELATION Example Correlation Partitioned Watershed Urban area Eigenvalues Eigenvectors Irrigation regions

24 Discriminant function
MULTIVARIATE MODEL Discriminant function Example Discriminant Calculation Villages Vehicles Test Structures

25 OPTIMIZATION MODEL OPTIMIZATION Dynamic Meanings Indirect Non-Linear
Simulation Objective function Minimization Constraints Experimentation Solution Examples Maximization Optimum Transportation Routes Optimum irrigation scheme Optimum Regional Spacing

26 MODELLING PROCESS Introduction Definition Modelling Validation
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

27 MODELLING PROCESSES HYPOTHESES Decision Table Relevance Processes
Relationships Variable Linkages Linear Impacts Non-Linear Species Interactive Sub-systems

28 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)

29 MODELLING PROCESSES VALIDATION Verification Critical Test
Sensitivity Analysis Subjectives Uncertainty Analysis Resources Objectivities Experiments Interactions Reasonableness

30 ROLE OF THE COMPUTER Introduction Speed Algoritms Data Program
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

31 ROLE OF THE COMPUTER DATA Machine readable Cautions Availability
Format Sampling Punched card Exchange Paper tape Format Reanalysis Magnetic Tape Data banks Disc

32 MODEL & MATHEMATICS