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

3

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

2

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

9

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

13

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

1

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

18

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: Jamie.Winter@mathworks.com

Phone: 508-647-7463

MathWorks

www.mathworks.com

Customer Service

Email: service@mathworks.com

Phone: 508.647.7000 option 1

Technical Support

Email: support@mathworks.com

Phone: 508.647.7000 option 2

25 © 2011 The MathWorks, Inc.