Engineering Problem Solving with Computers

1. Engineering Problem Solving with Computers MEPP Summer Residency August 2008

2. Outline for Session • About me • Course overview • Cases • Excel programming and Optimization • Matlab Primer

3. Intro • Jake Blanchard, Professor, Engineering Physics • PhD in Nuclear Engineering, UCLA, 1988 • Research: fusion technology, solid mechanics, nuclear batteries for MEMS, laser effects in metals • Born and raised in Southern California • married with two kids (11 and 9 yrs)

5. My Research Interests • Fusion Technology • Fission Reactor Fuels and Structures • Nuclear Microbatteries

6. Goal of EPSC • Students who have completed this course should have a broad understanding of: • Solution techniques for several equation types • Level of difficulty for various problem types • Appropriate tools for solving various problems • Advantages and disadvantages of using computers to solve engineering problems

7. Goal of This Session • I just want to get you started with the tools we use in my course • My theory is that some exposure now will benefit you in the Spring • We will repeat everything we do today when the course starts, though in more depth • Therefore, don’t worry if you don’t catch on to everything right away

8. Approach Used in EPSC • Problem-based using case studies • Assigned and student-identified projects • No exams

9. Textbooks • We will use a text I put together from two full texts: one Excel-based and one Matlab-based • You won’t all need this and no problems will be assigned from it • Buy it from Rose • Many other background books are available if you need additional support

10. Numerical Topics • Linear and nonlinear equations • Quadrature • Ordinary differential equations • initial value • boundary value • Optimization • Data Analysis • Databases

11. Prerequisites and Resources • Math skills: linear algebra (matrices and vectors) and ordinary differential equations (first and second order) • Computer skills: some programming is useful, but not necessary

12. Used These Before? • FORTRAN • C • C++ • Pascal • Basic • Java • Others? • EES • MathCAD • Matlab • Excel/Quattro • Mathematica • Maple • Others?

13. Tools • Microsoft Excel (97, 2000, 2003, etc.) • Matlab from Mathworks • there is a student version for ~ $100 • Any version beyond Matlab 4 will work fine, though a couple things got easier with version 6 and a few commands have changed • You can run it as “tethered” software from CAE if you are interested (www.cae.wisc.edu/tethered)

14. Cases • Broad coverage of engineering disciplines and topics • The more students can see relevance of cases, the better

15. Case Titles and Topics • Macros in Excel • Databases • Material Properties (choose your own for lesson) • Quadrature • Automobile suspension • Roots • natural frequencies of satellite boom • Linear Systems • fluid flow network

16. Case Titles and Topics • Initial Value • PSII target heating • Boundary Value • chip cooling • Optimization (Linear Programming/Constraints) • manufacturing

17. Case Titles and Topics • Optimization (Monte Carlo) • maximize profit with uncertain inputs • Curve Fits • radioactive decay

18. Hands-On Session • Optimization Problem in Excel (using the Solver) • Introduction to Matlab

19. First Download Files http://www.cae.wisc.edu/~blanchar/MEPP.html

20. Optimization of Water Distribution • Consider two bottling plants: Mexico City and Tepic • Consider three customers: one in Monterrey, one in Mazatlan, and the other in Acapulco • Question is: which plants should ship to which cities?

22. Plant Data

23. Customer Data

24. Best Guess • Use pencil and paper to make best guess of optimum distribution • Goal is to meet demand with minimum cost • Selling price is the same in each city

25. Sheet Setup What is total cost for your guess at the optimal distribution?

26. Using the Solver • Tools/Add-Ins…Solver • Tools/Solver • Take a look at this link for further information: http://econltsn.ilrt.bris.ac.uk/cheer/ch9_3/ch9_3p07.htm

27. The Main Solver Window

28. Dialog for Adding Constraints

29. Results Dialog

30. Your Task • Set up the Solver, with all appropriate constraints, to optimize this problem

31. Next Scenario • What if the production cost in Tepic drops to 0.45 $/gal?

32. Next Scenario • What is optimum if demand increases in each city by 50%? Put Tepic back at 0.6 $/gal on the production cost.

33. Adding a “Run” Button • Excel has a built-in macro language called Visual Basic for Applications (VBA) • It can be used to create user interfaces • We can use it to add a button for running the Solver

34. Using Macros • Macros are written in a Basic-like language called Visual Basic for Applications • Excel comes with a separate macro editor • To create or edit a macro, go to Tools/Macro/Visual Basic Editor • To add a new module go to Insert/Module

35. The Macro Sub runsolver() SolverSolve End Sub

36. Creating the Button • Go to View/Toolbars/Forms • From this Toolbar, click on the button (row 2, column 2) and then trace out a button on a spreadsheet • Assign the “runsolver” macro to the button • Now click the button • Note that you may have to add a “Reference” to the Solver under Tools in the VBA Editor

37. User-Defined Functions • We can also create user-defined functions in VBA • These can be called from cells, just like any built-in function

38. Creating a Function • Suppose we want to create an Excel function that takes a temperature in Celsius and converts to Fahrenheit • We would type the following in a module: Function ctof(temp) ctof = 9 / 5 * temp + 32 End Function

39. Using the function • Then you can go to the spreadsheet and type =ctof(100) • Or, you can put the value of “100” into cell A1 and then type =ctof(A1) into some other cell • In fact, this function can be used just as any built-in Excel function can be used

40. Exercise • Copy this function and create ftoc for converting from fahrenheit to celsius

41. The Macro Language • Operators: +, -, *, /, ^, Mod • Comparison: =, <, >, <=, >=, <> • Logical Operators: And, Eqv, Imp, Not, Or, Xor • Intrinsic Functions: Abs, Cos, Sin, Tan, Atn (arc tangent), Exp, Log (natural), Sgn, Sqr (square root), Rnd (random number)

42. Flow Control If condition Then statements Else statements End If If x=0 Then f=1 Else f=sin(x)/x End If

43. Flow Control For counter=start To end statements Next For i=1 To 100 sum=sum+i Next

44. Flow Control Do Until condition statements Loop i=1 x=1 Do Until i=50 x=x*i i=i+1 Loop

45. Flow Control Do While condition statements Loop i=1 x=1 Do While i<50 x=x*i i=i+1 Loop

46. Example • Write an Excel function that calculates the factorial of some number Z • Factorial is Z*(Z-1)*(Z-2)*…*3*2*1

47. My solution Function fact(Z) x = 1 ans = 1 Do Until x = Z ans = ans * x x = x + 1 Loop fact = ans End Function

48. Another Solution Function fact(Z) ans = 1 For i = 1 To Z ans = ans * i Next fact = ans End Function

49. Exercise • Write an Excel function that calculates the sum of the first N cubes and test it • That is: 13+23+33+…+N3 • What is the result for N=20?

50. Matlab • Matlab began as a linear algebra package • It’s grown to be a general purpose equation solver • Strengths: robust routines, excellent performance • Weaknesses: more difficult user interface