Mathematical Modeling using MATLAB, by U.M. Sundar Senior Application Engineer – Technical computing
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The document discusses mathematical modeling using MATLAB, addressing challenges, techniques, and applications in modeling real-world systems. It covers data-driven and first-principles approaches, as well as the use of parallel computing to handle large datasets and optimize calculations. Additionally, it outlines training and consulting services offered by MathWorks to enhance users' ability to leverage MATLAB tools effectively.
Mathematical Modeling using MATLAB, by U.M. Sundar Senior Application Engineer – Technical computing
- 1. 1 © 2012 The MathWorks, Inc. Mathematical Modeling using MATLAB U.M. Sundar Senior Application Engineer – Technical computing [email protected]
- 2. 2 Agenda • Challenges in Mathematical Modeling • Introduction to Mathematical Modeling Techniques • Mathematical Modeling of a Real World System • Deriving and Solving Governing Equations • Modeling Systems using Field Data • MathWorks Services an overview
- 3. 3 Challenges Getting from mathematical concepts to a software model Validation and optimization of the mathematical model against requirements Acquiring field data from files, field instruments, and test rigs Characterizing systems using field data Representing real-world datasets as optimized lookup tables Utilizing the power of multiple processing cores to speed up calculations Deploying models across a whole organization
- 4. 4 What is mathematical modeling? Use of mathematical language to describe a system or process Mathematical model Input Output 2 2 2 2 L x L n W q to l Lift on aircraft wing Electricity load ,...) , , ( DP t T f EL Some simple examples
- 5. 5 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
- 6. 6 Data-Driven Modeling First Principles Modeling Modeling Approaches Different Modeling Approaches
- 7. 7 Both have advantages & disadvantages Data-Driven Modeling First-Principles Modeling CompleteModeling Environment Advantages: Insight in behavior Physical parameters Disadvantages: Time-consuming Requires expertise Advantages: Fast Accurate Disadvantages: Requires plant Requires data acquisition system
- 8. 8 Modeling with Governing Equations (or) First Principles Modeling 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 x y E = V2 R Equations F = ma Algorithm Development Application Development
- 9. 9 Demo: Modeling aircraft wing loads Problem: Determine whether bending moments on aircraft wing are within design limit Workflow: Derive analytical models for wing loads and bending moment Simulate bending moment for different “what if” scenarios Analyze simulation results to determine whether worst-case bending moments are within design limit
- 10. 10 Demonstration: Analytical Modeling of Aircraft wing forces Load 1: Aerodynamic lift Load 2: Structural load Load 3: Fuel Load 1/2 1/2 l f /2 ql(x) qw(x) qf(x)
- 11. 11 Modeling with Governing Equations (or) First Principles Modeling 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 x y E = V2 R Equations F = ma Algorithm Development Application Development Automate
- 12. 12 Explore & Discover Data Driven Modeling Workflow Reporting and Documentation Outputs for Design Deployment Share Data Analysis & Modeling Algorithm Development Files Software Hardware Access Code & Applications Application Development
- 13. 13 Data Driven Modeling Using Statistical Methods Two common challenges in creating an accurate curve fit Can’t describe the relationship between your variables Can’t specify good starting points for your solvers
- 14. 14 Challenge 1 Generating a Good Fit Without Domain Knowledge
- 15. 15 Regression Techniques Require that the user specify a model Choice of model is based on domain knowledge Example - Population models Logistic Growth Exponential Growth
- 16. 16 What if you don’t know what type of model to use?
- 17. 17 Line ??? Quadratic ??? Rational ??? What if you don’t know what type of model to use?
- 18. 18 Workflow – Non-Parametric Fitting Share Explore and Create Data Access Report Application Files Software Curve Fitting Statistical Analysis Get the data to fit, into MATLAB Perform non-parametric curve fitting Cross validate using statistical methods Compare results Automatic publish Share MATLAB files
- 19. 19 Explore & Discover Data Driven Modeling Workflow Reporting and Documentation Outputs for Design Deployment Share Data Analysis & Modeling Algorithm Development Files Software Hardware Access Code & Applications Application Development Automate
- 20. 20 Solving Big Problems Large data set Problem Long running Computationally intensive Wait Load data onto multiple machines that work together in parallel Solutions Run similar tasks on independent processors in parallel Reduce size of problem You could…
- 21. 21 Task 1 Task 2 Task 3 Task 4 Task 1 Task 2 Task 3 Task 4 Task Parallel Applications Time Time TOOLBOXES BLOCKSETS Worker Worker Worker Worker
- 22. 22 Parallel Computing enables you to … 11 26 41 12 27 42 13 28 43 14 29 44 15 30 45 16 31 46 17 32 47 17 33 48 19 34 49 20 35 50 21 36 51 22 37 52 Speed Up Computations Workwith Large Data Task 1 Task 2 Task 3 Task 4 Task 4 Task 3 Task 2 Task 1
- 23. 23 MATLAB and ParallelComputing Tools Industry Libraries Message PassingInterface (MPI) Parallel Computing with MATLAB Built in parallel functionality within specific toolboxes (also requires Parallel Computing Toolbox) High level parallel functions Low level parallel functions Built on industry standard libraries matlabpool batch parfor jobs, tasks ScaLAPACK Optimization Toolbox Global Optimization Toolbox System Test Simulink Design Optimization Bioinformatics Toolbox Model-Based Calibration Toolbox Statistics Toolbox
- 24. 24 Writing Parallel Code Other toolboxes: Optimization Toolbox™ Genetic Algorithm and Direct Search Toolbox™ SystemTest™ parfor distributed arrays jobs and tasks MATLAB MPI No code changes Trivial changes
- 25. 25 MATLAB Desktop End-User Machine 1 2 3 Toolboxes Deploying MATLAB Models MATLAB Compiler .dll 25
- 26. 26 Give MATLAB code to other users Share applications with end users who do not have MATLAB – Use MATLAB Compiler to create standalone executables and shared libraries – Use MATLAB Compiler add-ons to create software components .exe .dll .lib MATLAB Compiler Java MATLAB Builder NE MATLAB Builder EX MATLAB Builder JA Deploying Applications with MATLAB
- 27. 27 Training Services Exploit the full potential of MathWorks products Flexible delivery options: Public training available in several cities Onsite training with standard or customized courses Web-based training with live, interactive instructor-led courses More than 30 course offerings: Introductory and intermediate training on MATLAB, Simulink, Stateflow, code generation, and Polyspace products Specialized courses in control design, signal processing, parallel computing, code generation, communications, financial analysis, and other areas www.mathworks.in/training
- 28. 28 Public Trainings in the next Few Months Course Dates Location Simulink for System and Algorithm Modeling 20 Aug 2012 – 21 Aug 2012 Bangalore EmbeddedCoderfor Production Code Generation 22 Aug 2012 – 24 Aug 2012 Bangalore MATLAB Fundamentals 03 Sep 2012 – 05 Sep 2012 Bangalore MATLAB Programming Techniques 06 Sep 2012 – 07 Sep 2012 Bangalore MATLAB Fundamentals 24 Sep 2012 – 26 Sep 2012 Pune Simulink for System and Algorithm Modeling 27 Sep 2012 – 28 Sep 2012 Pune Statistical Methodsin MATLAB 15 Oct 2012 – 16 Oct 2012 Bangalore MATLAB BasedOptimizationTechniques 17 Oct 2012 Bangalore Stateflow for Logic-Driven System Modeling 18 Oct 2012 – 19 Oct 2012 Bangalore Email: [email protected] URL: http://www.mathworks.in/services/training Phone: 080-6632-6000
- 29. 29 Consulting Services www.mathworks.com/consulting A global team of experts provide support from initial project startup through integrated process automation to increase productivity and maximize the value of product investments Supplier Involvement ProductEngineeringTeams Migration Planning Component Deployment Full Application Deployment Adv Engineering Continuous Improvement Research Advisory Services Process Establishment/ Assessment Jumpstart Process & Technology Standardization Process & Technology Automation
- 30. 30 MATLAB for Quantitative Tools to Manage Risk Challenge Intuitive Analytics wanted to develop a set of quantitative tools that minimizes the expected costor risk a government incurs when managing a capital structure. Solution (with the help of MathWorks’Consulting) Able to use MathWorks tools to develop algorithms, visualize results, and simplify deploymentof an advanced analytical tool Value Developmentproductivity increased by 90% Deploymentsimplified Visual environment created For more information: http://www.mathworks.com/tagteam/51834_91408v02_intutive.pdf Using MATLAB development tools to provide visual representations of interest rate models. “I estimate that we can develop 90% faster with MathWorks tools than we could with C/C++ or Visual Basic.” - Peter Orr, Intuitive Analytics, Inc. Using MATLAB developmenttools to provide visual representations of interest rate models
- 31. 31 MathWorks India Contact Details URL: http://www.mathworks.in E-mail: [email protected] Technical Support: www.mathworks.in/myservicerequests Tel: +91-80-6632 6000 Fax: +91-80-6632 6010 • MathWorks India Private Limited Salarpuria Windsor Building Third Floor, 'A' Wing No.3 Ulsoor Road Bangalore - 560042, Karnataka India Thank You for Attending Talk to Us – We are Happy to Support You