Mathematical Modeling using MATLAB - MathWorks

1 Mathematical Modeling using MATLAB . Sundar Senior Application Engineer Technical computing 2012 The MathWorks , 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 2. 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 3. What is Mathematical Modeling ? Use of Mathematical language to describe a system or process Input Output Mathematical model Some simple examples 2 Wto n L2 x 2. ql . L2 EL f (T , t , DP.)

2 Lift on aircraft wing Electricity load 4. 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 5. Different Modeling Approaches Modeling Approaches First Principles Modeling Data-Driven Modeling 6. Both have advantages & disadvantages Complete Modeling Environment Data-Driven Modeling First-Principles Modeling Advantages: Advantages: Fast Insight in behavior Accurate Physical parameters Disadvantages: Disadvantages: Requires plant Time-consuming Requires data acquisition system Requires expertise 7. Modeling with Governing Equations (or). First Principles Modeling Access Explore & Create Share Files Reports and Data Surface fitting Data Analysis Report Documentation Mathematical Application Software Modeling V2 Applications x E= y R.

3 Algorithm Development Equations Derivation & solving Report Hardware Application Development Outputs for Design Optimization Application Equations F = ma 8. 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 9. Demonstration: Analytical Modeling of Aircraft wing forces ql(x). Load 1: Aerodynamic lift 1/2. 1/2. Load 2: Structural load qw(x). l f /2. Load 3: Fuel Load qf(x) 10. Modeling with Governing Equations (or). First Principles Modeling Access Explore & Create Share Files Reports and Data Surface fitting Data Analysis Report Documentation Mathematical Application Software Modeling V2 Applications x E= y R. Algorithm Development Equations Derivation & solving Report Hardware Application Development Outputs for Design Optimization Application Equations F = ma Automate 11.

4 Data Driven Modeling Workflow Access Explore & Discover Share Files Reporting and Data Analysis Documentation & Modeling Algorithm Software Outputs for Design Development Code & Applications Application Development Hardware Deployment 12. Data Driven Modeling using Statistical Methods Two common challenges in creating an accurate curve fit Can't describe the relationship Can't specify good starting points between your variables for your solvers 13. Challenge 1. Generating a Good Fit Without Domain Knowledge 14. Regression Techniques Require that the user specify a model Choice of model is based on domain knowledge Example - Population models Logistic Growth Exponential Growth 15. What if you don't know what type of model to use? 16. What if you don't know what type of model to use? Line ??? Quadratic ??? Rational ??? 17. Workflow Non-Parametric Fitting Get the data to fit, into Perform non-parametric Automatic publish MATLAB curve fitting Share MATLAB files Cross validate using statistical methods Compare results Data Access Explore and Create Share Curve Report Fitting Statistical Analysis Application Files Software 18.

5 Data Driven Modeling Workflow Access Explore & Discover Share Files Reporting and Data Analysis Documentation & Modeling Algorithm Software Outputs for Design Development Code & Applications Application Development Hardware Deployment Automate 19. Solving Big Problems Problem You could Solutions Long running Run similar tasks on independent Computationally Wait processors in intensive parallel Load data onto Reduce size Large data set multiple machines of problem that work together in parallel 20. Task Parallel Applications Worker TOOLBOXES. Worker Worker BLOCKSETS. Worker Task 1 Task 2 Task 3 Task 4. Time Time 21. Parallel Computing enables you to . Speed Up Computations Work with Large Data 11 26 41. 12 27 42. 13 28 43. 14 29 44. 15 30 45. 16 31 46. 17 32 47. 17 33 48. Task 1 Task 2 Task 3 Task 4 19 34 49. 20 35 50. 21 36 51. 22 37 52. 22. Parallel Computing with MATLAB . Optimization Toolbox Global Optimization Calibration Toolbox Statistics Toolbox Simulink Design Bioinformatics Built in parallel functionality Model-Based Optimization System Test Toolbox Toolbox within specific toolboxes (also requires Parallel Computing Toolbox).

6 MATLAB and Parallel Computing Tools High level parallel functions parfor matlabpool batch Low level parallel functions jobs, tasks Built on industry Industry Libraries standard libraries Message Passing Interface (MPI). ScaLAPACK. 23. Writing Parallel Code No code changes Other toolboxes: Optimization Toolbox . Genetic Algorithm and Direct Search Toolbox . SystemTest . Trivial changes parfor distributed arrays jobs and tasks MATLAB MPI. 24. Deploying MATLAB Models 3. Toolboxes 1 MATLAB End-User Desktop Machine MATLAB . 2 Compiler .dll 25. 25. Deploying Applications with MATLAB . Give MATLAB code to other users MATLAB Compiler Share applications with end users who do not MATLAB MATLAB . Builder JA. MATLAB . Builder NE. Builder EX. have MATLAB . Use MATLAB Compiler to create standalone executables and .dll .exe .lib Java shared libraries Use MATLAB Compiler add-ons to create software components 26. 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 27.

7 Public Trainings in the next Few Months Course Dates Location Simulink for System and Algorithm Modeling 20 Aug 2012 21 Aug 2012 Bangalore Embedded Coder for Production Code 22 Aug 2012 24 Aug 2012 Bangalore Generation 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 Methods in MATLAB 15 Oct 2012 16 Oct 2012 Bangalore MATLAB Based Optimization Techniques 17 Oct 2012 Bangalore Stateflow for Logic-Driven System Modeling 18 Oct 2012 19 Oct 2012 Bangalore Email: URL: Phone: 080-6632-6000. 28. Consulting Services 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 Continuous Improvement Process & Technology Automation Process & Technology Standardization Full Application Deployment Process Establishment/ Component Assessment Deployment Advisory Services Jumpstart Migration Planning Research Adv Engineering Product Engineering Teams Supplier Involvement 29.

8 MATLAB for Quantitative Tools to Manage Risk I estimate that we can develop 90% faster Challenge with MathWorks tools than we could with C/C++ or Visual Basic. - Peter Orr, Intuitive Intuitive Analytics wanted to develop a set of quantitative tools Analytics, Inc. that minimizes the expected cost or 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 deployment of an advanced analytical tool using MATLAB development tools to provide visual Value representations of interest rate Development productivity increased by 90% models. Deployment simplified Visual environment created using MATLAB development tools to provide visual representations of interest rate models For more information: 30. MathWorks India Contact Details URL: E-mail: Technical Support: Tel: +91-80-6632 6000. Fax: +91-80-6632 6010. MathWorks India Private Limited Salarpuria Windsor Building Third Floor, 'A' Wing Ulsoor Road Bangalore - 560042, Karnataka India Thank You for Attending Talk to Us We are Happy to Support You 31.