Transcript A Core Course on Modeling

A Core Course on Modeling
1
Introduction to Modeling
0LAB0 0LBB0 0LCB0 0LDB0
AUD 3 Kees van Overveld
[email protected]
AUD 6 Tijn Borghuis
[email protected]
A Core Course on Modeling
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What is the mathematical model of a yoyo?
A Core Course on Modeling
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What is the mathematical model of a yoyo?
Answer: JJ=2D+T
A Core Course on Modeling
Week 1- No Model Without a Purpose
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Lesson 1
no model
without
a purpose
A Core Course on Modeling
Week 1- No Model Without a Purpose
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Two types of purposes:
• I want to know something
• I want to achieve something
A Core Course on Modeling
Week 1- No Model Without a Purpose
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Two types of purposes:
• I want to know something: research
• I want to achieve something: design
A Core Course on Modeling
Week 1- No Model Without a Purpose
     Purposes related to research    
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Purposes related to research    
1. Why does a yoyo ...
•
… climb the rope?
•
… go down slower than with 9.8 m/s2?
•
… attract so much fans?
Explanation: why is something as it is?
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Purposes related to research    
2. When will the yoyo ...
•
… reach its highest point?
•
… stop yoyoing?
•
… get out of fashion?
Prediction (1): at what time will X happen?
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Purposes related to research    
3. What will happen if ...
•
… I pull up the rope later?
•
… the diameter of the yoyo increases?
•
… a new toy comes to the market?
Prediction (2): what will happen if X?
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Purposes related to research    
4. How can I organize data?
r1(cm)
2.5  0.1
2.0  0.1
2.5  0.05
3.0  0.2
1.0  0.1
5  0.1
4  0.2
....
r2(cm)
5  0.2
8  0.1
5.10.1
6  0.1
10  0.2
1  0.1
4  0.2
m(kg)
a(m/s2)
0.2  0.05
0.3  0.05
0.5  0.02
0.3  0.05
0.6  0.05
0.1  0.05
0.3  0.05
3.3  0.2
1.4  0.5
3.2  0.1
3.2  0.4
0.2  0.05
9.8  0.3
7.4  0.2
r2
r1
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Purposes related to research    
12
4. How can I organize data?
r1(cm)
2.5  0.1
2.0  0.1
2.5  0.05
3.0  0.2
1.0  0.1
5  0.1
4  0.2
....
r2(cm)
5  0.2
8  0.1
5.10.1
6  0.1
10  0.2
1  0.1
4  0.2
m(kg)
a(m/s2)
0.2  0.05
0.3  0.05
0.5  0.02
0.3  0.05
0.6  0.05
0.1  0.05
0.3  0.05
3.3  0.2
1.4  0.5
3.2  0.1
3.2  0.4
0.2  0.05
9.8  0.3
7.4  0.2
r2/r1
2
4
2
2
10
0.2
1
A Core Course on Modeling
Week 1- No Model Without a Purpose
     Purposes related to research    
a (m/s2)
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10
3.3  0.2
1.4  0.5
3.2  0.1
3.2  0.4
0.2  0.05
9.8  0.3
7.4  0.2
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a(m/s2)
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4. How can I organize data?
2
4
a = 2g / (2+r22/r12)
2
4
6
8
10
r2/r1
Compression: how to compactly represent data?
r2/r1
2
4
2
2
10
0.2
1
A Core Course on Modeling
Week 1- No Model Without a Purpose
     Purposes related to research    
5. Focus on what is important:
•
Is the shape important?
•
Is the rope quality important?
•
Is the brand important for the nr. sold yoyo’s?
Abstraction: restrict to essentials
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Purposes related to research    
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6. Relate similar things:
•
In what respect does a yoyo resemble a bouncing ball?
•
In what respect does a yoyo resemble a hula hoop?
•
In what respect does a yoyo hype resemble any other hype?
Unification: find commonalities among different things
A Core Course on Modeling
Week 1- No Model Without a Purpose
     Purposes related to research    
7. Investigate ...
•
... the changing force in the rope
•
... the importance of friction
•
... how yoyo-popularity varies with the season
Analysis: seek relations within the modeled system
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Purposes related to research    
7. Investigate ...
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lin. height
lin. velocity
lin. acceleration
ang. velocity ()
ang. rotation ()
tijd
Analysis: seek relations within the modeled system
A Core Course on Modeling
Week 1- No Model Without a Purpose
     Purposes related to research    
8. Verify ...
•
... that the rope will be strong enough
•
... that energy is conserved
•
... that marketing laws apply to yoyo sales
Verification: ascertain the truth of something
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Purposes related to research    
9. Inform people ...
•
... how a yoyo works
•
... how to set up yoyo experiments
•
... how yoyo hype spreads
Communication: give comprehensible information
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Purposes related to design    
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Purposes related to design    
1. What options exist for ...
•
... shapes of yoyo’s
•
... tricks with yoyo’s
•
... marketing strategies to spawn hypes
Exploration: make inventory of options
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Purposes related to design    
2. How to decide ...
•
... what diameters to have yoyo rise more than 1 m
•
... what mass to have a stable yoyo
•
... what marketing price to get turnover better than X
Decision: what intervention needed to achieve goal
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Purposes related to design    
3. How to optimize ...
•
... diameters to have yoyo rise as far as possible
•
... mass to have yoyo as stable as possible
•
... marketing price to get turnover as large as possible
Optimization: what intervention give maximal result
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Purposes related to design    
4. How to instruct ...
•
... manufacturer to assemble a yoyo
•
... yoyo kid to perform trick X
•
... shop owner to put yoyo’s on display
Specification: ensure something will be as it should
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Purposes related to design    
5. How to ...
•
... have a robot operate a yoyo
•
... have an intelligent yoyo stabilize itself
•
... have shop order yoyo’s dependent on market demand
Control: adapting behavior to circumstances
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Purposes related to design    
6. How to ...
•
... have a yoyo simulator help learning tricks
•
... have a hype simulator train sales people
•
...
Train: familarize trainees with a system
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Various Kinds of Modeling Purposes     
Purposes from research
• Explanation
• Prediction (2)
• Compression
• Abstraction
• Unification
• Analysis
• Verification
• Communication (Documentation)
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Various Kinds of Modeling Purposes     
Purposes from design:
• Exploration
• Decision
• Optimization
• Specification
• Steering and Control
• Training
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Various Kinds of Modeling Purposes     
Q: Why is purpose important for the
modeler?
A: The answer to
any question in
modeling will be: ‘check your purpose’
almost
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     How models work     
• Question
• Question
• Data, Measurements
• Data, Measurements
• Calculations, Approximations
• Calculations, Approximations
• Conclusion
• Conclusion
• Consequences
• Consequences
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Modeling Approaches: material / immaterial     
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19th century brain model, Boerhaave Museum
20th century brain model (Wang & Chiew, UofCalgary, 2010)
A Core Course on Modeling
Week 1- No Model Without a Purpose
     Modeling Approaches: static / dynamic     
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Modeling Approaches: continuous / discrete     
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Modeling Approaches: numerical / symbolic     
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3 x 5 + 3 x 6 = 3 x (5+6) = 33
a x b + a x c = a x (b+c) = ?
A Core Course on Modeling
Week 1- No Model Without a Purpose
     Modeling Approaches: geometric / non geometric     
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Modeling Approaches: deterministic / stochastic     
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Modeling Approaches: calculating / reasoning     
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Modeling Approaches: black box/ glass box     
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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Modeling Approaches - overview     
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Material – Immaterial
Static – Dynamic
Continuous – Discrete
Numerical – Symbolic
Geometric – Non-geometric
Deterministic – Stochastic
Calculating – Reasoning
Black box – Glass box
typically, several of
these dimensions are
relevant for any given
model
A Core Course on Modeling
Week 1- No Model Without a Purpose
     Modeling Approaches - overview     
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dynamical
systems
data
modeling
process
modeling
modling from
scratch
Material – Immaterial
M Im
M Im
M Im
M Im
Static – Dynamic
St Dy
St Dy
St Dy
St Dy
Continuous – Discrete
Co Di
Co Di
Co Di
Co Di
Numerical – Symbolic
Nu Sy
Nu Sy
Nu Sy
Nu Sy
Geometric – Non-geometric Geo Ng Geo Ng Geo Ng Geo Ng
Deterministic – Stochastic
Det Sto Det Sto Det Sto Det Sto
Calculating – Reasoning
Cal Rea Cal Rea Cal Rea Cal Rea
Black box – Glass box
Bb Gb
Bb Gb
Bb Gb
Bb Gb
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
http://www.visade.nl/nieuws/2008/mailing__de_verkeerde_volgorde
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A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
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define
context  initial problem
conceptualize
initial problem  conceptual model
formalize
conceptual model  formal model
execute
conclude
formal model  result
result  resolve initial problem?
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
define
conceptualize
formalize
execute
conclude
sometimes, all
modeling phases
may be skipped
43
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
define
conceptualize
formalize
execute
conclude
sometimes, the
formal phases
may be skipped
44
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
define
formulate
purpose
conceptualize
formalize
execute
conclude
45
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
define
formulate
purpose
conceptualize
formalize
execute
conclude
identify
choose
entities
relations
46
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
formulate
define
purpose
conceptualize
formalize
execute
conclude
identify
choose
entities
relations
obtain
formalize
values
relations
47
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
formulate
define
purpose
conceptualize
formalize
execute
conclude
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
48
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
formulate
define
purpose
conceptualize
formalize
execute
conclude
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
49
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
50
formulate
define
purpose
conceptualize
formalize
execute
conclude
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
reflecting
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
formulate
define
51
Right problem?
purpose
conceptualize
formalize
execute
conclude
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
(problem validation)
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
formulate
define
52
Right problem?
purpose
conceptualize
identify
choose
entities
relations
(problem
validation)
Right concepts?
(concepts validation)
formalize
execute
conclude
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
formulate
define
53
Right problem?
purpose
conceptualize
formalize
execute
conclude
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
(problem
validation)
Right concepts?
(Right
concepts
validation)
model?
(model verification)
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
formulate
define
54
Right problem?
purpose
conceptualize
formalize
execute
conclude
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
(problem
validation)
Right concepts?
(Right
concepts
validation)
model?
(Right
modeloutcome?
verification)
(outcome verification)
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
formulate
define
55
Right problem?
purpose
conceptualize
formalize
execute
conclude
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
(problem
validation)
Right concepts?
(Right
concepts
validation)
model?
(Right
modeloutcome?
verification)
(outcome verification)
Right answer?
(answer verification)
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
Why is the modeling process relevant?
image: http://funnyjunk.com/comment/anonymous/content/4097630/-5/1/parent_id/20/3
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A Core Course on Modeling
Week 1- No Model Without a Purpose
   Summary    
57
• A model  clearly defined purpose;
• purposes are: explanation, prediction (two cases!), compression, abstraction, unification, communication,
documentation, analysis, verification, exploration, decision, optimization, specification, training, steering and
control.
• Modeling dimensions:
•material – immaterial : does the model have a physical component?
•static – dynamic: does time play a role?
•continuous - sampled - discrete: 'counting' or 'measuring'?
•numeric - symbolic: manipulating numbers or expressions?
•geometric - non-geometric: do features from 2D or 3D space play a role?
•deterministic - stochastic: does
probability
play a role?
after
the party…
•calculating - reasoning: rely on numbers or on propositions?
•black box - glass box: start from data or from causal mechanisms?
• Modeling is a process involving 5 stages:
•define: establish the purpose
•conceptualize: in terms of concepts, properties and relations
•formalize: in terms of mathematical expressions
•execute: running the model to obtain an outcome
•conclude: adequate presentation and interpretion
A Core Course on Modeling
Week 1- No Model Without a Purpose
   Study Guide    
What next:
•Come to lectures (presentations ‘lecture support’)
•Self study (presentations ‘self study’)
•For details: ‘lecture notes’
•For self-testing: questions in lecture notes
•For quick reference:
glossary
/ index
after
the party…
•For details on mathematics: ‘relation wizard’ and
‘function selector’ (week 4)
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A Core Course on Modeling
Week 1- No Model Without a Purpose
   Study Guide    
59
Homework:
•Assignment announced on Tuesday
•Find the assignment at ‘take home assignment’
•Every take home assignment contains an example
elaboration
•Submission deadline:
23:59
afterThursday
the party…
•Submissions must be PDF to PEACH
•Identification (name, ID, major) on page 1 – and nothing else
•Rest must be anonymous
A Core Course on Modeling
Week 1- No Model Without a Purpose
   Study Guide    
60
Peer Reviewing:
•Collect review bundle from PEACH: review assignment
•Review assistance: ‘review assistance’
•Typically, you receive 5 assignments to review
• Scores: number on a scale 0 … 50
after the
party…
• Ranking: put works
in order,
best (top) to worst (bottom)
•Submit reviews to PEACH: deadline Sunday 23:59
A Core Course on Modeling
Week 1- No Model Without a Purpose
   Study Guide    
Group assignment:
•visit specific lectures (Wednesday or Friday)
•study specific material
(different for 0LAB, 0LBB, 0LCB, 0LDB)
•meetings with supervisors
after the
party…
•write report using ‘report
template’
•3 feedbacks, based on ‘assignment rubrics’
61
A Core Course on Modeling
Week 1- No Model Without a Purpose
   Study Guide    
Marking:
•30 %: average result of take home assignments
•10 %: quality of reviewing
•60 %: group assignment
• 10 %: first feedback
the party…
• 10 %: second after
feedback
• 40 %: final feedback
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A Core Course on Modeling
Week 1- No Model Without a Purpose
   Study Guide    
63
Recommended time spending:
•2 h/w 7 x 2
= 14h generic lectures or study self-study presentations
•1 h/w 7 x 1
= 7h studying, self-testing
•3 h/w 7 x 3
= 21h take home assignment
•1.5 h/w 7x1.5  11h peer reviewing
•2 h/w 7 x 2
= 14h specific lectures
•1 h/w 7 x 1
after the party…
= 7h studying
•1 h/w 8 x ?
= 6h meetings with supervisors
•7 h/w 8 x 7
= 56h group work
----------
136 h  5 EC