Presentasi sedang didownload. Silahkan tunggu

Presentasi sedang didownload. Silahkan tunggu

MODEL & MATHEMATICS DR. HERI NUGRAHA. SE. MSi. WHAT IS SYSTEM MODELLING ? Recognition Definitions Problems Evaluation Identification Feed-back Solution.

Presentasi serupa


Presentasi berjudul: "MODEL & MATHEMATICS DR. HERI NUGRAHA. SE. MSi. WHAT IS SYSTEM MODELLING ? Recognition Definitions Problems Evaluation Identification Feed-back Solution."— Transcript presentasi:

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

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

3 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

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

5 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

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

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

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 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 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. 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 PARAMETER: Nilai-nilai karakteristik dari populasi KONSTANTE, KOEFISIEAN: nilai-nilai karakteristik yang dihitung dari SAMPEL

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 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. 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 Language Equations Computer General Special DYNAMO CSMP CSSL DYNAMO CSMP CSSL BASIC FORMAL ANALYSIS

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

26 MODELLING PROCESS Introduction Definition System analysis Integration Hypotheses Conclusion Modelling Validation Model Processes Bounding Word Models Alternatives Systems Impacts Space Time Niche Elements Space Time Niche Elements Factorial Confounding Factorial Confounding Separate Combinations Separate Combinations Communication Data Analysis Choices Test Estimates Plotting Outliers Plotting Outliers

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

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 Objectivities Subjectives Experiments Reasonableness Sensitivity Analysis Analysis Interactions Uncertainty Resources

30 ROLE OF THE COMPUTER Introduction Speed Roles Conclusions Data Development Algoritms Reasons Speed Data Algoritm Speed Data Algoritm Comparison Implication Waste Techniques Errors Plotting Techniques Errors Plotting Manual Calculator Computer Manual Calculator Computer Repetition Checking Repetition Checking 9/10 Modelling 9/10 Modelling Programming Program Language Information High level Special Machine code FORTRAN BASIC ALGOL FORTRAN BASIC ALGOL DYNAMO. Etc.

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

32 MODEL & MATHEMATICS


Download ppt "MODEL & MATHEMATICS DR. HERI NUGRAHA. SE. MSi. WHAT IS SYSTEM MODELLING ? Recognition Definitions Problems Evaluation Identification Feed-back Solution."

Presentasi serupa


Iklan oleh Google