This presentation is a powerpoint presentation dealing with concepts of modeling and simulation.

1. Modeling & Simulation
Lectures

2. Define a model as :
A representation of an object, a system or
an idea in some form other than that of
the entity itself.

3. Why are model used ?
• To Test a system without having to create the system for real (Building
real-life systems can be expensive, and take a long time)
• To Predict what might happen to a system in the future (An accurate
model allows us to go forward in virtual time to see what the system
will be doing in the future)
• To Train people to use a system without putting them at risk (Learning
to fly an airplane is very difficult and mistake will be made. In a real
plane mistakes could be fatal!)
• To Investigate a system in great detail (A model of a system can be
zoomed in/out or rotated. Time can be stopped, rewound, etc.)

4. Disadvantages
• The results depend on how good the model is and how much data was used to create it in the first place.
• Models and simulations can't ever completely re-create real- life situations.
• Not every possible situation may have been included in the model.
• The equipment and software are expensive to purchase.
• Staff need to be trained how to use the software and equipment.

5. Simulation
Simulation is the process of designing a model of a real system and
conducting experiments with this model for the purpose of either
understanding the behavior of the system and/or evaluating various
strategies for the operation of the system."
equipment.

6. • The technique of imitating the behavior of some situation or system by
means of an analogous model, situation, or apparatus, either to gain
information more convenient) or to train personnel.
• Simulation:
— "... as a strategy — not a technology — to mirror, anticipate, or
amplify real situations with guide( experiences in a fully interactive
way."

10. World War II
"Monte Carlo" simulation: originated with the work on the atomic
bomb. Used to simulate bombing raids. Give the security code
name "Monte-Carlo".
Late '50s, early '60s
First languages introduced: SIMSCRIPT, GPSS (IBM)
Late '60s, early '70s
GASP IV introduced by Pritzker. Triggered a wave of diverse
applications. Significant in the evolution of simulation.

11. Late 70s Early 80s
• SLAM introduced in 1979 by Pritzker and Pegden.
• Models more credible because of sophisticated tools
• SIMAN introduced in 1982 by Pegden. First language to run on both a
mainframe as well as a microcomputer.
Late `80s through present
• Powerful PCs • Languages are very sophisticated (market almost
saturated)
• Major advancement: graphics. Models can now be animated!

12. Advantages of simulation
• New policies, operating procedures, information flows and son on can be explored
without disrupting ongoing operation of the real system.
• New hardware designs, physical layouts, transportation systems and ... can be tested
without committing resources for their acquisition.
• Time can be compressed or expanded to allow for a speed-up or slow-down of the
phenomenon( clock is self-control).
• Insight can be obtained about interaction of variables and important variables to the
performance.
• Bottleneck analysis can be performed to discover where work in process, the system
is delayed.
• A simulation study can help in understanding how the system operates.
• "What if" questions can be answered.

13. • A simulation study can help in understanding how the system operates.
• "What if" questions can be answered
Disadvantages of simulation
1. Model building requires special training.
• Vendors of simulation software have been actively developing packages that
contain models that only need input (templates).
2. Simulation results can be difficult to interpret.
• Simulation modeling and analysis can be time consuming and expensive.
• Many simulation software have output-analysis.

14. Modeling
There are few key factors in a modeling scheme for the appropriate representation of a model:
1. Competence: if a model is not adequate to describe a complete interest in the system than this
model may not fulfil the required or intended objectives.
2. Simplicity: contrary to competence, a model must be simple; if a simpler model is possible then
one must try to represent accordingly. There may be states of a system that are not required to
describe the complete or unnecessary details.
3. Causality: the system may be dependent upon different inputs or requirements that must be
considered appropriately.
4. Redundancy: This refers to variables or states that can be avoided because some other variables is
doing the similar and required work. But reliable systems have some redundancy because if one fails
to deliver, the other may help to achieve the objective.

15. TYPES OF MODELING
There are numerous types of modeling within the M&S toolbox that range from the mathematical to the hybrid:
Physics-based modeling is solidly grounded in mathematics. A physics based model is a mathematical model where the
model equations are derived from basic physical principles. Unique to physics-based models is the fact that the physics
equations are models themselves in that many physics-based models are not truly things, but intangibles; hence, they are
representations of phenomena.
Finite element modeling (FEM) is the method for modeling large or complicated objects by decomposing these
elements into a set of small elements and then modeling the small elements. This type of modeling is widely used for
engineering simulation, particularly, mechanical and aerospace engineering. These sub disciplines conduct research that
requires structural analysis or fluid dynamics problems. FEM facilitates the decomposition of a large object into a set of
smaller objects labeled elements.
Data-based modeling results from models based on data describing represented aspects of the subject of the model.
Model development begins with advanced research or data collection, which is used in simulations. Data sources for this
type of modeling can include actual field experience via the real-world or real system, operational testing and evaluation
of a real system, other simulations of the system, qualitative and quantitative research, as well as best guesses from
subject matter experts (SMEs). The model is developed with the view that the system is exercised under varying
conditions with varying inputs. As the outputs unfold, their results are recorded and tabulated so as to review appropriate
responses whenever similar conditions and inputs are present in the model.

16. Multi scale Modeling refers to a style of modeling in which multiple models at different scales are used
simultaneously to describes a system. Different models usually focus on different scales of resolution. For example:
quantum mechanical model and level of molecular dynamics.
Mathematical modeling is a description of a system using mathematical concepts and language. Models are used in
natural sciences and engineering disciplines.
Hybrid modeling entails combining more than one modeling paradigm. This type of modeling is becoming common
practice among model developers. Hybrid modeling makes use of several modeling methods; however, they are
disadvantaged in that composing several different types of models correctly is a difficult process.

17. Qualitative Aspects
• Model Requirements

19. Quantitative Aspects
These requirements and observations will play a role in interface design and model code
implementation and in mathematical modeling.
It also consider the quantitative aspect of system behavior that have to be included in the
mathematical model.
For the model input and output variables, following ahs to select:
• Select a symbol.
• Assign a unit and use it to specify typical ranges and resolutions.
• Specify bandwidths

20. Conceptual Model
• A conceptual model that reflects internal structure of the system in term of its subsystem and
networks of idealized system components.
Block Diagram
To set up a basic model of a normal cardiorespiratory system, specifically study the effect of oxygen
metabolism in body tissues on spontaneous breathing and systemic arterial and venous blood gasses,
leading to the input and output variables reflected in the block diagram.

21. • Its further specify that the model should include spontaneously breathing lungs, distribution of the
respiratory gasses by the circulation, metabolism in the body tissues and control of breathing which
maintains arterial blood gasses at appropriate values by adjusting respiratory muscle activity.
• An intuitive graphical representation of these structures and processes is included as:

22. • There are certain criteria for separating systems into subsystems:
First criteria
• The lungs and the airways are anatomically separate form the overall system.
• Blood reaches the lungs via the pulmonary arteries and leaves via the pulmonary veins.
• The partial pressure of the respiratory gases oxygen and carbon dioxide in those vessels are: Po2pa (t), P Co2
pa (t), Po2pv (t) and P Co2pv (t) respectively.
• The input variable, oxygen metabolism is represented by, mO2(t).
• Lets further assume that the respiratory muscles responsible for spontaneous breathing receives nervous
activity with the firing frequency fmus(t).
• Breathing and ventilation are reflected in the time-varying alveolar volume Va(t)

23. • Anatomical hierarchies often provide a first basis for identifying subsystems
• Second criteria for separating a system into sub system is based on function rather than
structures or on physiology rather than anatomy.
• Examples of physiological processes includes formation, transport, transformation and absorption
of substances and generation, transmission and processing of signals.
• The lungs represents a single anatomical structure but cm be further divided into lung mechanics
involving volume transports and pulmonary gas exchange involving solute transport in the volume
carrier and diffusion between gas and blood.

25. • Third criteria for separating system into subsystem is measurability of input output variables.
• Measurability facilities interpretation and system identification, but meaningful system may
sometimes rely on input-output variables that are difficult or impossible to measure directly.

26. Component Diagram
• Even if meaningful casually connected subsystem can no longer be distinguished, it may be able to
describe the internal structure and functioning of a system further in terms of interacted components
connected in a network.
• Overall system behavior depends on the properties of the components and on how they are connected.
• Generally, physiological systems do not consist of discrete components connected in a network, however,
component diagrams are derived mathematical models may represent system properties and behavior in a
reasonable approximations.
• Setting up a conceptual model of a physiological system in the form of a component diagram is an
inductive, creative process where simplifying assumptions need to balanced against anticipated models and
performances.

28. Mathematical Models
• A mathematical model is derived form a conceptual model in the form of a component diagram.
• This steps involves formulating and combining natural or empirical laws describing components
and connections.
Example # 1

30. Example # 2

34. The state space model of Linear Time-Invariant (LTI) system can be represented as,
X˙=AX+BU
Y=CX+DU
The first and the second equations are known as state equation
and output equation respectively.
Where,
•X and X˙ are the state vector and the differential state vector respectively.
•U and Y are input vector and output vector respectively.
•A is the system matrix.
•B and C are the input and the output matrices.
•D is the feed-forward matrix.

35. State
It is a group of variables, which summarizes the history of the system in order to predict the future values
(outputs).
State Variable
The number of the state variables required is equal to the number of the storage elements present in the
system.
Examples − current flowing through inductor, voltage across capacitor
State Vector
It is a vector, which contains the state variables as elements.

36. Consider the following series of the RLC circuit.
It is having an input voltage, vi(t) and the current flowing through the circuit is i(t).
There are two storage elements (inductor and capacitor) in this circuit. So, the number of the state variables is
equal to two and these state variables are the current flowing through the inductor, i(t) and the voltage across
capacitor, vc(t).
From the circuit, the output voltage, v0(t) is equal to the voltage across capacitor, vc(t).

37. Vo(t) = Vc(t)
Apply KVL around the loop
The voltage across the capacitor is -

38. Differentiate the above equation with respect to time.
We can arrange the differential equations and output equation into the standard form of state space model
as,

40. Direct Representation of Fluid Circuits

43. Direct Representation of Gas uptake
and
Distribution