MODEL & MATHEMATICS DR. HERI NUGRAHA. SE. MSi

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

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 Tipe Konstante Variabel Parameter Likelihood Dependent Populasi Probability Analitik Independent Maximum Sampel Simulasi Regressor

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

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

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

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 Dynamics SIMULATION Equations Computer FORMAL Language ANALYSIS Special General DYNAMO CSMP CSSL BASIC

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

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

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

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

STOCHASTIC MODEL STOCHASTIC Probabilities History Other Models Statistical method Dynamics Stability

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

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

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

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

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

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

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

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

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

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

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

MODELLING PROCESSES HYPOTHESES Decision Table Relevance Processes Relationships Variable Linkages Linear Impacts 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 Sensitivity Analysis Subjectives Uncertainty Analysis Resources Objectivities Experiments Interactions Reasonableness

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

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

MODEL & MATHEMATICS