Transcript Engineering 1000 Chapter 3: Problem Formulation

Engineering 1000
Chapter 6: Abstraction and Modeling
Outline
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Why is abstraction useful?
What are models?
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Examples from microelectronics
Types of model
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how are models different from theory and simulation?
finite element models
Approximations and responsibility
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Abstraction 2
Abstraction
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“Abstraction” has the same root meaning as the abstract of a
report
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The purpose of abstraction is to enable the designer to
consider the relative merits of several options without having
to build prototypes of each one
By formulating the problem in the ways that we have already
considered …
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to summarise and extract the essential elements
from the Oxford English Dictionary: “the act or process of separating in
thought, of considering a thing independently of its associations”
especially the objective/function trees
… we have already moved some way along the road to
abstraction
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the generation of multiple options is sometimes referred to as parsing
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Abstraction 3
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The advantage of the tree diagrams is that closely related
issues are automatically identified
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and some idea of their ‘level’ has been obtained
this is effectively a second stage of abstraction
it is worth checking to see if objectives at the same level but on
different branches of the tree can be achieved using a common method
In our objectives tree, we stopped one stage before developing
ways of implementing those objectives
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in abstraction, we now need to consider what these possible
implementations will be
to do this we need to shuffle around concepts, find relations, identify
commonalities, consider variations, …,
i.e. manipulate the elements of the problem
the textbook calls this the “dimensions of variation”
the statement-restatement technique was one way of achieving this
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What is a Model?
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A model is a representation or imitation of a real object
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in engineering terms, a model is used because it enables predictions or
calculations or in some other way makes the design process more
convenient
often, the model is a mathematical description which can be
manipulated by computer
but it can also be a physical model of an object, which maintains a
desired characteristic (e.g. the shape of a car) but is in some way
simpler than the real thing (e.g. no internal machinery)
Traditionally, models are small-scale versions of bridges,
buildings, planes, etc.
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which are tested in order to predict how the real structure would
behave under appropriate conditions
this is not always easy because some effects do not scale linearly with
distance (e.g. friction, fluid flow)
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Models as Purposeful Representations
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The textbook uses the words “purposeful representation” as a
brief definition of a model
Models are used to assist the designer’s thinking, analyse
potential designs, realise what is known or unknown, predict
behaviour, identify connections, etc.
Models are typically used when the system is incompletely
understood
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the textbook also states that models are used for complex systems
However, we must distinguish here between physical models
and computer-based models
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physical models are indeed used for complex systems, and represent
one of engineering’s oldest tools
complex and understood systems are usually solved by simulation in
computer-based approaches (see later for an example)
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How is a Model Different from Theory?
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A model is related to, but different from, a theoretical
description of the object
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the model may be based on theory
but may include non-ideal behaviours observed in experiments but not
well explained by theory
theory may predict certain trends, but empirical numbers from
experiments are included to get the calculated results to agree with the
real results
The key difference is that a model must behave as nearly as
possible the same way as the real thing
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but it is not directly important whether the model’s behaviour is well
predicted by theory – it is the result that counts
[a good theoretical basis is good however, because it will likely expand
the range of conditions over which the model will work]
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How is a Model Different from Simulation?
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A simulation is usually a technique for obtaining theoretical
results in cases where the theory is mathematically tough to
solve
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so simulation is a practical way of solving the theoretical description
assuming you know the appropriate theory!
It can help to think of the difference between a model plane
and a flight simulator!
We will illustrate these situations with an example from
microelectronics
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Abstraction 8
Microelectronic Circuit Design
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The goal here is to predict as closely as possible the
behaviour of a microelectronic circuit design before it is
manufactured
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There are a number of levels which we must consider
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e.g. amplifier gain, bandwidth, distortion, logic gate switching time
the circuit operation
the components which make up the circuit (transistors, resistors,
capacitors, diodes, interconnects)
the physical mechanisms within each of these components
the way in which the manufacturing process affects the behaviour
It is not always necessary for the designer to understand all of
these levels in depth
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but the computer software must assume this knowledge
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Abstraction 9
SPICE Circuit Simulator
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SPICE is a widely used circuit analysis package which allows
the designer to connect electronic devices into a circuit
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and predicts the response of the circuit under specified conditions
SPICE is a circuit simulator
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www.silvaco.com
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it applies circuit analysis equations to the designed circuit to calculate
currents and voltages as a function of time
for any condition, it may require a lot of calculations to reach a final
answer where all the values are internally consistent
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But how does SPICE ‘know’ how a transistor behaves?
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SPICE Models
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SPICE contains an analytical model of how every device
behaves
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There are numerous ‘levels’ of models depending on how
complex they are
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i.e. how accurately they describe every aspect of the device behaviour,
no matter how subtle
It is not directly important for SPICE models to be theoretically
accurate
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‘analytical’ means mathematically solvable
the basic characteristics are described by theory
but many complexities are based on observations of extensive
experimental data
these are empirical or semi-empirical models
This is very important, because it means that the accuracy of
your predictions are highly dependent on how much you know
about the specific devices in your circuit
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www.silvaco.com
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Microelectronic manufacturing ‘fabs’ will measure thousands
of devices in order to get accurate SPICE models
A widely used SPICE model for transistors is BSIM 3.3
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The better the theoretical framework, the more generally
applicable will be the results
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and the model can be refined
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Device Simulators
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Most of the basic theory for semiconductor devices is well
known
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Device simulators such as MEDICI sub-divide the device into
elements which are simulated individually but consistently
with neighbouring elements
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elements are of varying size to capture details where needed but to
save computation time elsewhere
www.avanticorp.com
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however, applying it to a realistic device is extremely complex (sound
familiar? – same as SPICE)
this is because the 3-D geometry of the devices and the any material
layers they contain makes hand calculation impossible
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As with all simulators, the results are only as good as your
theoretical understanding of the situation
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In the end, engineers like theory to the extent that it improves
the models
www.avanticorp.com
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but a design must still work even if there is no adequate theory
and so (good) models are of paramount importance
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Computer-Aided Design (CAD)
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Many engineering projects would be impossible to realise
without CAD
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CAD is rather a loose term which may range from fancy graphics
packages to complex software suites including modelling and
simulation
e.g. the 10 million transistors in the Pentium would not be feasible if
paced and connected by hand (much is done with automatic layout)
A common tool for laying out chips is CADENCE
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it contains a ‘drawing’ package for defining metal, silicon, etc layers
a ‘design rule’ checker
SPICE
automatic layout
‘standard cells’
and numerous other tools
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AutoCad
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Another standard CAD
package is AutoCad
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which you will learn in
part 2 of ENG1000
www.autodesk.com
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Computer-Aided Manufacture (CAM)
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The logical conclusion of CAD is CAM
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By using the data generated by the CAD tools directly for
controlling the machines manufacturing the item several
benefits follow
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and the two are often lumped together as CAD/CAM
speed
accuracy – no (additional) errors introduced
flexibility
For example, we email output files from CADENCE to the chip
manufacturing plant
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one of the advantages of standardisation of information formats
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Types of Model
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Models can be categorised into three basic types
Iconic models
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Analogic models
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look identical to the finished object; visually equivalent
e.g. maps, globes, computer graphics, physical models
but are incomplete in the sense that some information is lost
e.g. a 2-D representation of a 3-D object, no internal mechanics
are functionally equivalent to the object
so they behave like the real object, but not necessarily for the same
reasons
e.g. the transistor models in SPICE, model aeroplane in a wind tunnel
Symbolic models
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such as descriptions using mathematical (or chemical) equations
e.g. postscript representation of a font, x2 + y2 = r2
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Finite Element Models
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The mesh used to analyse electronic devices in MEDICI is an
example of a finite element model (FEM)
FEMs are used in many situations where the basic equations
are known but are very difficult to solve in more than one
dimension and for complex situations
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heat flow = (thermal conductivity) x (temperature gradient)
electrical currents as a function of electric field
fluid flow as a function of pressure gradients
stresses in complex surfaces
For each element the equations are solved
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ensuring that conditions match at boundaries between adjacent
elements
‘boundary’ conditions are satisfied
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One general FEM solver is ANSYS
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www.ansys.com
mesh
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stresses
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Approximations
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It should be remembered at all times that models and
simulations are all approximations to reality
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The engineer must understand
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they may use simplifying assumptions (i.e. models)
unknown effects cannot be included
equations may be solved by numerical methods, which do not yield
exact results
often, models are only valid over a specific range of conditions,
especially is they are semi-empirical (use measured data)
the theory, models, and techniques on which the solution is based
nature of the approximations used in the model
the situations for which the technique is valid
There is no substitute to experience with a particular modelling
tool
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often engineers ‘know’ when a particular tool gives good or bad results
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Responsibility
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The performance of the design is engineer’s responsibility,
regardless of how the design was carried out
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errors in simulation or modelling are also the engineer’s responsibility,
not that of the software vendor
From the PEO:
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The practice of professional engineering has become increasingly reliant on computers, and
engineers use many computer programs that incorporate engineering principles and
matters. Many of these programs are based upon or include assumptions, limitations,
interpretations and judgments on engineering matters that were made by or on behalf of an
engineer when the program was first developed. Therefore, it is often difficult to determine,
just by using a program or by being given a description of its function, the engineering
principles and matters it incorporates. The engineer must have a suitable knowledge of the
engineering principles involved in the work being conducted, and is responsible for the
appropriate application of these principles. When using computer programs to assist in this
work, engineers should be aware of the engineering principles and matters they include,
and are responsible for the interpretation and correct application of the results provided by
the programs. Engineers are responsible for verifying that results obtained by using
software are accurate and acceptable. Given the increasing flexibility of computer software,
the engineer should ensure that professional engineering verification of the software's
performance exists. In the absence of such verification, the engineer should establish and
conduct suitable tests to determine whether the software performs what it is required to do.
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Developing a Model
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Developing good models is a difficult and time-consuming
process
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this is perhaps not surprising since the complexity of the situation is the
likely reason for needing a model in the first place
a large proportion of engineering research is devoted to the
development and improvement of models
How do you know it’s a good model?
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ultimately, it must be verified by favourable comparison with a wide
range of experimental results collected by different people under a
variety of appropriate conditions
‘goodness’ depends on the requirements of the specific situation
by repeated successful trials, some measure of confidence can be
established in the tool
a corollary is that software modelling tools are the domain of a few wellestablished companies in each engineering field
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Summary
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Theory, simulation, and modelling are tools to enable the
engineer to understand and to predict the behaviour of
proposed designs
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without having to construct prototypes
The advantage is that various options can be considered and
compared as efficiently as possible
The disadvantage is that no model/simulation/theoretical
description is exact
It is the engineer’s responsibility to ensure that these tools are
used appropriately
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Homework
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Read chapter 6 of the textbook and the case studies described
in that chapter
Do problems 6.1 and 6.2
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Exercise
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Develop a simple model governing the number of economyclass seats in an aeroplane
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as a function of other relevant factors (e.g. ticket price)
can you optimise the number?
What assumptions have you made in your model?
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it is always important to state explicitly all your assumptions, so users
of the model know if it is valid for their situation
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