mathematical modeling with matlab...
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1 © 2011 The MathWorks, Inc.
Mathematical Modeling with
MATLAB Products
2
From MathWorks
Jamie Winter
– Senior Sales Manager
Abhishek Gupta
– Application Engineer
Loren Shure
– MATLAB Technical Consultant
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Overview of mathematical modeling
Mathematical modeling with MATLAB
Black box modeling
First-principles modeling
Summary
Agenda
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What is mathematical modeling?
Use of mathematical language to describe a
system or process
Mathematical
model
Input Output
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222
L
xLnWq to
l
Lift on aircraft wing Electricity load
,...),,( DPtTfEL
Some simple examples
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Why develop mathematical models?
Forecast system behavior
Predict and gain insight into system
behavior for various “what-if” scenarios
– Enables critical decisions
– Reduces the need for testing
Optimize system behavior
Identify parameters that optimize
system performance
Design control systems
Develop model to represent plant
during control system design
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Demos
Predicting concrete strength (black box)
– Non-parametric regression (trees)
– Ensemble methods and feature selection
Optimizing gantry crane motion (first principles)
– Symbolic derivation of equations of motion
– Optimize system behavior
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Technical Computing with MATLAB Products
Equations
Data Surface fitting
Share Access Explore & Create
Derivation & solving
Optimization
Report
Application
Report
Application
Share Access
Reports and
Documentation
Outputs for Design
Applications
Explore & Create
Data Analysis Files
Hardware
Software Mathematical
Modeling
Algorithm
Development
Application
Development
x y E = V
R
Equations
F = ma
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Overview of mathematical modeling
Mathematical modeling with MATLAB
Black box modeling
First-principles modeling
Summary
Agenda
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Predicting Concrete Strength
Predict concrete measured compressive
strength for a given composition
and age
Ash,...)Slag,FlyFurnaceBlast
r,Cement,f(Age,WateStrength
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Decision Trees
For use when relationship
between predictors and
response is unknown
Set of if-then statements
that lead to a prediction
Can be used in aggregate
to improve predictive accuracy
Bagging (bootstrap aggregation)
uses many trees created from
resampling data set
1 if Age<21 then node 2 elseif Age>=21
then node 3 else 35.7928
2 if Cement<354.5 then node 4 elseif
Cement>=354.5 then node 5 else 23.3874
3 if Cement<355.95 then node 6 elseif
Cement>=355.95 then node 7 else 41.3278
4 fit = 18.3255
5 fit = 34.9657
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Predicting Concrete Strength
Develop non-parametric model
– Decision trees
Improve the model accuracy
– Bootstrap aggregation (Bagging)
Determine optimal subset of features
– Sequential feature selection
– In parallel, for performance
Products Used MATLAB
Statistics Toolbox
Parallel Computing Toolbox
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Overview of mathematical modeling
Mathematical modeling with MATLAB
Black box modeling
First-principles modeling
Summary
Agenda
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Modeling Gantry Crane
Determine acceleration profile
that minimizes payload swing
s20s4
s15s1
s15s1
:sConstraint
2
1
21
f
p
p
ppf
t
t
t
ttt
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MATLAB Desktop
End-User Machine
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2
3 Toolboxes
Deploying Applications with MATLAB
MATLAB Compiler
.exe
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Java Excel .NET Web
Deploying Applications with MATLAB
Give MATLAB code
to other users
Share applications
with end users who
do not need MATLAB
– Stand-alone
executables
– Shared libraries
– Software components
.exe .dll
.lib
MATLAB Compiler
MATLAB Builder NE
MATLAB Builder EX
MATLAB Builder JA
Explore & Discover Share Access
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Modeling Gantry Crane
Derive equations of motion
– Symbolic math notebook
Determine ideal acceleration profile
– ODE solver
– Constrained minimization
Find all possible solutions
– Multi-start search
– In parallel, for performance
Generate stand-alone application
Products Used MATLAB
Symbolic Math Toolbox
Optimization Toolbox
Parallel Computing Toolbox
MATLAB Compiler
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Overview of mathematical modeling
Mathematical modeling with MATLAB
Black box modeling
First-principles modeling
Summary
Agenda
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Mathematical Modeling with MATLAB
Equations
Data Surface fitting
Share Access Explore & Create
Derivation & solving
Optimization
Reports
Applications
Nonparametric regression
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Building Mathematical Models in MATLAB Toolboxes Extend Breadth of Modeling Tools
Diverse modeling techniques
– Deriving symbolic expressions
– Fitting distributions
– Linear and nonlinear regression
– Machine learning (e.g. neural networks,
decision trees)
– Solving PDEs, ODEs
Domain-specific
– Financial (e.g. portfolio optimization, risk modeling)
– Biological (e.g. pharmacokinetics, systems biology)
Bond pricing model
Pharmacokinetic
model
Neural network for time series data fitting
Weibull distribution for
modeling wind speed
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Modeling with Simulink and Stateflow Complex Multidomain and Multirate Systems
Block-diagram environment
Dynamic, linear and
nonlinear systems
Hierarchical / component-based
Full access to MATLAB
Platform for controls, signal processing,
and communications
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MATLAB for Mathematical Modeling
Explore and integrate different
modeling approaches
Use built-in functions for fitting,
optimization, and statistics
Automate simulation and
post-processing analysis
Generate reports, applications,
and software components
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Lund University Develops an Artificial
Neural Network for Matching Heart
Transplant Donors with Recipients
Challenge Improve long-term survival rates for heart transplant
recipients by identifying optimal recipient and donor
matches
Solution Use MathWorks tools to develop a predictive artificial
neural network model and simulate thousands of risk-
profile combinations on a 56-processor computing
cluster
Results Prospective five-year survival rate raised by up
to 10%
Network training time reduced by more than two-
thirds
Simulation time cut from weeks to days
“I spend a lot of time in the clinic, and
don’t have the time or the technical
expertise to learn, configure, and
maintain software. MATLAB makes it
easy for physicians like me to get
work done and produce meaningful
results.”
Dr. Johan Nilsson
Skåne University Hospital
Lund University Link to user story
Plots showing actual and predicted survival, best and worst donor-
recipient match, best and worst simulated match (left); and survival
rate by duration of ischemia and donor age (right).
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Learn More about Mathematical Modeling with
MATLAB Products
MATLAB Digest: Accelerating Finite
Element Analysis in MATLAB with
Parallel Computing
Recorded webinar: Electricity
Load and Price Forecasting with
MATLAB
Symbolic Math Toolbox Web demo:
Modeling the Power Generated by a
Wind Turbine
MATLAB Digest: Improving an
Engine Cooling Fan Using Design for
Six Sigma Techniques
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Thank You for Attending Today’s Seminar
Jamie Winter
Senior Account Manager
Email: [email protected]
Phone: 508-647-7463
MathWorks
www.mathworks.com
Customer Service
Email: [email protected]
Phone: 508.647.7000 option 1
Technical Support
Email: [email protected]
Phone: 508.647.7000 option 2
25 © 2011 The MathWorks, Inc.