Modeling and Simulation - Engineering Perspectives - Lecture Slides, Slides of Process Engineering

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Introduction to modeling,

simulation, and Optimization

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Systems

• What is System
  • A system is a set of components which are related by some form of interaction and which act together to achieve some objective or purpose - Components are the individual parts or elements that collectively make up the system - Relationships are the cause-effect dependencies between components - Objective is the desired state or outcome which the system is attempting to achieve

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Systems

• Natural vs. Artificial Systems
  • A natural system exists as a result of processes occurring in the natural world (e.g. river, universe)
  • An artificial system owes its origin to human activity (e.g. space shuttle, automobile)
• Static vs. Dynamic Systems
  • A static system has structure but no associated activity (e.g. bridge, building)
  • A dynamic system involves time-varying behavior (e.g. machine, U.S. economy)

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Systems

• Open-Loop vs. Closed-Loop systems
  • Inputs
    • Variables that influence the behavior of the system
      • e.g. wheel, accelerator, and brake of a car
  • Outputs
    • Variables that are determined by the system and may influence the surrounding environment - e.g. direction and speed of a car
  • An open-loop system cannot control or adjust its own performance - e.g. watch, car
  • A closed-loop system controls and adjusts its own performance in response to outputs generated by the system through feedback - e.g. watch with owner, car with driver
  • Feedback is the system function that obtains data on system performance (outputs), compares the actual performance to the desired performance (a standard or criterion), and determines the corrective action necessary Docsity.com^5

Models

• What is Model
  • A model of a system is a representation of the construction and working of the system
  • Similar to but simpler than the system it represents
    • Close approximation to the real system and incorporate most of its salient features
    • Should not be so complex that it is hard to understand or experiment with it
• Physical Model
  • A physical object that mimics some properties of a real system
    • e.g. During design of buildings, it is common to construct small physical models with the same shape and appearance as the real buildings to be studied
  • Through prototyping process
    • Prototyping is the process of quickly putting together a working model (a prototype) in order to test various aspects of a design, illustrate ideas or features and gather early user feedback (^7) Docsity.com

Models

• Mathematical Model
  • A description of a system where the relationship between variables of the system are expressed in a mathematical form - e.g. Ohm's law describes the relationship between current and voltage for a resistor; Hooke's Law gives the relationship between the force applied to an unstretched spring and the amount the spring is stretched when the force is applied, etc.
  • Through virtual prototyping
  • Deterministic vs. stochastic models
    • In deterministic models, the input and output variables are not subject to random fluctuations, so that the system is at any time entirely defined by the initial conditions chosen - e.g. the return on a 5-year investment with an annual interest rate of 7%,compounded monthly
    • In stochastic models, at least one of the input or output variables is probabilistic or involves randomness - e.g. the number of machines that are needed to make certain parts based on theprobability of machine failure

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Simulation

• What is Simulation
  • A simulation of a system is the operation of a model of the system, as an imitation of the real system
  • A tool to evaluate the performance of a system, existing or proposed, under different configurations of interest and over a long period of time - e.g. a simulation of an industrial process to learn about its behavior under different operating conditions in order to improve the process
• Reasons for Simulation
  • Experiments on real systems are too expensive, too dangerous, or the system to be investigated does not yet exist - e.g. Investigating ship durability by building ships and letting them collide is a very expensive method of gaining information; training nuclear plant operators in handling dangerous situations by letting the nuclear reactor enter hazardous states is not advisable (^) Docsity.com^10

Simulation

• Reasons for Simulation (Cont.)
  • The time scale of the dynamics of the system is not compatible with that of the experimenter - e.g. It takes millions of years to observe small changes in the development of the universe, whereas similar changes can be quickly observed in a computer simulation of the universe
  • Easy manipulation of parameters of models (even outside the feasible range of a particular physical system) - e.g. The mass of a body in a computer-based simulation model can be increased from 40 to 500 kg at a keystroke, whereas this change might be hard to realize in the physical system
  • Suppression of disturbances (^) Docsity.com 11

Phases and Steps of Simulation

• Phase 1. Develop Simulation Model
  • Step 1. Identify the problem
  • Step 2. Formulate the problem
  • Step 3. Collect and process real system data
  • Step 4. Formulate and develop a model
  • Step 5. Validate the model
  • Step 6. Document model for future use
• Phase 2. Design and Conduct Simulation

Experiment

• A test or series of tests in which meaningful changes are made to the input variables of a simulation model soDocsity.com^13

Simulation

• Phase 3. Perform Simulation Analysis
  • Step 10. Analyze data and present results
  • Step 11. Recommend further courses of actions

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Develop Simulation Model

• Step 3. Collect and Process Real System Data
  • Collect data on system specifications, input variables, performance of the existing system, etc.
  • Identify sources of randomness (stochastic input variables) in the system
  • Select an appropriate input probability distribution for each stochastic input variable and estimate corresponding parameters - Standard distributions (e.g. normal, exponential, etc.) - Empirical distributions - Software packages for distribution fitting (e.g. @Risk, Arena, Matlab, etc.) (^) Docsity.com^16

Develop Simulation Model

• Step 4. Formulate and Develop a Model
  • Develop schematics and network diagrams of the system
    • How do entities flow through the system
  • Translate conceptual models to simulation software acceptable form
  • Verify that the simulation model executes as intended
    • Build the model right (low-level checking)
    • Traces
      • Vary input parameters over their acceptable ranges and check the output

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Design and Conduct Simulation

Experiment

• Step 7. Select Appropriate Experimental Design
  • Performance measures
  • Input parameters to be varied
    • Ranges and legitimate combinations
  • Document experiment design
• Step 8. Establish Experimental Conditions for Runs
  • Whether the system is stationary (performance measure does not change over time) or non-stationary (performance measure changes over time)
  • Whether a terminating or a non-terminating simulation run is appropriate (^) Docsity.com 19

Simulation Analysis

• Step 10. Analyze Data and Present Results
  • Statistics of the performance measure for each configuration of the model - Mean, standard deviation, range, confidence intervals, etc.
  • Graphical displays of output data
    • Histograms, scatterplot, etc.
  • Document results and conclusions
• Step 11. Recommend Further Courses of Actions
  • Other performance measures
  • Further experiments to increase the precision and reduce the bias of estimators (^) Docsity.com^20