Post on 06-Dec-2015
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Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 1
Ammar Mushtaq ammar.mushtaq@rcms.nust.edu.pk
Research Center for Modeling and Simulation (RCMS)National University of Sciences and Technology (NUST)
Islamabad, Pakistan
Course Outline
Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 2
Comparison of System Designs
Analysis of Variance
Variance Reduction Techniques
Design of Experiments
Introduction to Simulations
Types of Simulation Models
Simulation Examples
Monte-Carlo Simulations
Response Surface Methods
Classical Optimization Theory
Unconstrained Optimization
Constrained Optimization
MODELING & SIMULATION
EVALUATION OF DESIGN
BEST SOLUTION
Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 3
Probability & Statistics
Pre-requisites & Books
Discrete-Event Simulation (A first course)by S. Park & L. Leemis
Statistical Quality Controlby Douglas C. Montgomery
Simulation Modeling & Analysisby Averill M. Law
Linear Algebra & Calculus
Programming & MATLAB
Evaluation
Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 4
Quizzes (06) 10-15%
Assignments (03) 05-10%
OHT’s (02) 30-40%
End Term 40-50%
3-0 Course (~ 45 Lec)
>75%
ATTENDANCE
MARKS DISTRIBUTION
Simulation has emerged as the
THIRD METHODOLOGY
of exploring the truth It would complement the theory and experimental
methodology
Simulation will never replace them!!
M & S?
Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 5
Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 6
Ways to Study?
Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 7
System
Experiment with Actual System
Experiment with Model of the System
SimulationAnalytical Solution
Mathematical Model
Physical Model
Models Types
Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 8
System model
Deterministic Stochastic
StaticDynamic Static Dynamic
ContinuousDiscrete Continuous Discrete
Monte Carlosimulation
Discrete-eventsimulation
Discrete-eventsimulation
ContinuoussimulationContinuoussimulation
Discrete-eventsimulation
Discrete-eventsimulation
ContinuoussimulationContinuoussimulation
Linear and Nonlinear
Models Types
Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 9
Stochastic
• Model that contains random (probabilistic) elements,
• Examples
Inter-arrival time or service time of customers at a restaurant or store
Amount of time required to service a customer
• Output is a random quantity (multiple runs required analyze output)
Deterministic
• Model containing no random elements
• Examples
Simulation of a digital circuit
Simulation of a chemical reaction
• Output is deterministic for a given set of inputs
Models Types
Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 10
Static
• Model where time is not a significant variable
• Examples
Determine the probability of a winning solitaire hand
• Static + stochastic = Monte Carlo simulation
Statistical sampling to develop approximate solutions to numerical problems
Dynamic
• Model focusing on the evolution of the system under investigation over time
Typically represented by differential equations.
Models Types
Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 11
Discrete
• State of the system is viewed as changing at discrete points
in time
• An event is associated with each state transition
Events contain time stamp
Continuous
• State of the system is viewed as changing continuously
across time
Velocity of fluid in pipe flows
Temperatures and stresses in a solid
Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 12
Define goals, objectives of study
Develop conceptual model
Develop specification of model
Develop computational model
Verify model
Validate model
Fundamentally an iterative process
Model Development Cycle
Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 13
• What does you (or the customer) hope to accomplish with the model
Predict the weather
Train personnel to develop certain skills (e.g., driving)
Optimize a manufacturing process or develop the most cost effective means to reduce traffic congestion in some part of a city
• Often requires developing a business case to justify the cost
— Improved efficiency will save the company $$$
Example: electronics
• Objectives may not be known when you start the project!
— One often learns things along the way
Objective & Goals
Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 14
• An abstract (i.e., not directly executable) representation of the
system
• What are state variables?
• How are they interrelated?
• Which variables should be included in model?
• What can be left out?
• Level of detail
• Appropriate choice depends on the purpose of the model
Conceptual Model
Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 15
• A more detailed specification of the model including more
specifics
• Collect data to populate model
— Traffic example: Road geometry, signal timing, expected traffic demand,
driver behavior
— Empirical data or probability distributions often used
• Development of algorithms necessary to simulate the system
— Example: Path planning for vehicles
Specification Model
Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 16
Computational Model
• Executable simulation model
• Software approach
— General purpose programming language
— Special purpose simulation language
— Simulation package
— Approach often depends on need for customization and economics
Where do you make your money?
Defense vs. commercial industry
• Other (non-functional) requirements
— Performance
— Interoperability with other models/tools/data
Verification
Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 17
• Did I build the computational model right?
• Does the computational model match the specification model?
• Largely a software engineering activity (debugging)
• Not to be confused with correctness (see model validation)!
Validation
Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 18
• Did I build the right model?
• Does the computational model match the actual (or envisioned)
system?
• Typically, compare against
― Measurements of actual system
― An analytic (mathematical) model of the system
― Another simulation model
• By necessity, always an incomplete activity!
— Often can only validate portions of the model
— If you can validate the simulation with 100% certainty, why build the
simulation?
Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 19
Knowledge of the system under investigation (Domain Expert)
System analyst skills (model mathematical formulation)
Model building skills (model programming)
Data collection skills
Statistical skills (input data representation)
More statistical skills (output data analysis)
Even more statistical skills (Design of Experiments/ANOVA/Optimization)
Management skills (to get everyone pulling in the same directions)
M & S Team Skills
Summary
Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 19
• Modeling and simulation is an important, widely used technique with
a wide range of applications
― Computation power increases (Moore’s law) have made it more universal
― In some cases, it has become essential (e.g., to be economically competitive)
― Rich variety of types of models, applications, uses
• As easy (actually, easier!) to get wrong or misleading answers as it is to
get useful results
• Appropriate methodologies required to protect against major mistakes