Modeling & Simulation Flashcards
George Box
Statistician responsible for several breakthroughs in the areas of experimental design, time series analysis, and statistical modeling (Box-Cox Transformation, Box-Behnken Design, and Box-Jenkins Methodology)
The quote “All models are wrong, some models are useful” is attributed to George Box.”
Model
an abstract representation of a system
Simulation
Simulation is the process of (1) developing a system model & (2) conducting experiments with this model for the purpose of understanding the behavior of the system or evaluating various strategies for the operation of the system
It is an imitation of system performance over time to a predefined degree of fidelity
– design analyses (model the system & the environment)
– breadboards (model the system)
– qualification testing (models the environment)
– training (models the mission)
The “Real World”
Consists of Problems and Actions
The “Model World”
Consists of the Model and Results
Models must be validated and have the appropriate levels of fidelity
Results must be meaningful and verified
Model Scope
Model Breadth
Model Generality
“Model Breadth” v. “Model Generality”
Model Depth
Model Fidelity
Model Realism
“Model Fidelity” v. “Model Realism”
Model Precision
Tradeoff between generality and realism
Model Accreditation
1) Face Validity
2) Peer Review
3) Functional Decomposition
4) Comparison or Empirical Validation
Classes of System Models
1) Continuous Systems
2) Discrete-time Systems
3) Hybrid Systems
Continuous Systems v. Discrete-time Systems
Continuous - Variables change continuously with respect to time
Discrete - Variables only change at distinct/finite instants of time
*There are also Hybrid systems which have elements of both
Deterministic v. Stochastic Models
Both are types of Statistical Models
Deterministic - Non-probabilistic relationships between system variables
– Tend to be continuous systems; typified by mathematical models
* lift of an airplane wing
* thrust of a rocket engine
Stochastic - Probabilistic relationships between system variables
– Tend to be discrete-time systems; typified by random discrete event models
* wind velocities encountered by a flight vehicle during ascent
* component failures during system operation
Model Building Process
1) FIND
2) FACTORS
- Exogeneous variables
- Endogenous variables
- Assumptions
3) MODEL SELECTION
- Based on what can be measured/calculated
4) MODEL VERIFICATION
Simulation Building Process
1) Build a model
2) Strategic & Tactical Planning
3) Experimentation
4) SME Validation
5) Analysis of Results
Model Building tips
1) Simpler models are better. Simplify wherever you can
2) Only develop a model to answer a question. No modeling for the sake of modeling
3)
Four types of models
1) Physical Models: Tangible representations of objects or systems
2) Graphical Models: Represent systems or relationships between elements using visual elements such as charts, graphs, or diagrams
3) Mathematical Models: Rely on equations, algorithms, and mathematical structures to represent systems and processes quantitatively
4) Statistical Models: Represent systems based on probabilistic relationships between variables, often developed from empirical data
Physical Models
Definition: Physical models are tangible representations of objects or systems. They are usually scaled versions, prototypes, or replicas that allow for hands-on interaction and observation.
Purpose: Used for visualizing complex structures and testing physical properties in real-world conditions. They are often applied in engineering, architecture, and product design.
Examples: Wind tunnel models of airplanes, architectural scale models, and anatomical models in medicine.
Advantages: Provide a concrete understanding and direct interaction, useful for testing physical forces and dynamics in prototypes.
Limitations: Expensive and time-consuming to build, not easily adjusted for hypothetical scenarios or scaling variables
Graphical Models
Definition: Graphical models represent systems or relationships between elements using visual elements such as charts, graphs, or diagrams. They illustrate complex interactions in an accessible, visual format.
Purpose: Used to communicate relationships, dependencies, and hierarchies among components. Common in fields like systems engineering, project management, and network analysis.
Examples: Flowcharts, network diagrams, UML diagrams, and decision trees.
Advantages: Simple to interpret, useful for identifying patterns, connections, and bottlenecks, and ideal for presenting to stakeholders.
Limitations: Limited quantitative analysis capabilities and can be overly simplified, failing to capture all system nuances
Mathematical Models
Definition: Mathematical models use equations, algorithms, and mathematical structures to represent systems and processes quantitatively. They are designed to predict behavior and provide solutions based on input variables.
Purpose: Used to analyze and predict outcomes by quantifying relationships between variables, often involving formulas or complex calculations. Common in physics, economics, and engineering.
Examples: Newton’s laws of motion, economic supply-demand models, and fluid dynamics equations.
Advantages: Precise and capable of handling complex, dynamic systems; useful for optimization and predictive analysis.
Limitations: Requires accurate data and assumptions; can be challenging to interpret for non-technical stakeholders
Statistical Models
Definition: Statistical models represent systems based on probabilistic relationships between variables, often developed from empirical data. These models are used to make inferences or predictions about real-world phenomena.
Purpose: Used for data analysis, risk assessment, and forecasting by evaluating patterns and correlations in data. Commonly applied in data science, finance, and healthcare.
Examples: Linear regression models, ARIMA models for time series forecasting, and logistic regression for classification.
Advantages: Useful for dealing with uncertainty, analyzing trends, and making data-driven predictions.
Limitations: Dependent on quality and quantity of data; prone to inaccuracies if assumptions about data distribution or correlations are incorrect
Monte Carlo Simulations
Type of Statistical model
Linear Regression Modeling
Type of Statistical model
Logistic regression modeling
Type of Statistical model
ARIMA models for time series forecasting
Type of Statistical model
