Spreadsheet Techniques and Problem Solving for ChEs

Transcription

1 AIChE Webinar Presentation Problem Solving for ChEs David E. Clough Professor Dept. of Chemical & Biological Engineering University of Colorado Boulder, CO :00 p.m. EDT, 27 October Problem Solving for ChEs Outline of Presentation setting up Excel a couple suggestions selection, copying and moving rapid techniques creating formulas using cell and range names suggestions on creating engineering graphs case studies using Data Table targeting calculations using Goal Seek optimizing with constraints using Solver 2 1

2 setting up Excel a couple suggestions o one worksheet in a new workbook o move selection after enter cancel lit o make sure you have Solver and Data Analysis add-ins else Problem Solving for ChEs 3 selection, copying and moving rapid techniques o making jumps around the spreadsheet double -click Ctrl- o selecting blocks of data quickly o copying also F5 key adjoin Shift key also Ctrl-a or Ctrl-* for entire block to jump technique hold down Ctrl for selections that are not contiguous edge with Ctrl make selection o moving Ctrl-c select destination Ctrl-v also drag and drop make selection Ctrl-x select destination Ctrl-v also Problem Solving for ChEs 4 2

3 selection, copying and moving rapid techniques o using Autofill for an index column double -click the Fill Handle can drag it out, but not useful for long columns o creating a free-standing index column starting index Problem Solving for ChEs 5 creating formulas using cell and range names o build formulas using pointing more reliable start formula with = point to n and click build rest of formula using pointing status bar o Enter mode and Edit mode double-click cell or F2 In Edit mode, can use End and Home also arrow keys to move within formula. In Enter mode, those keys point to cells. toggle between and with F2 Problem Solving for ChEs 6 3

4 creating formulas using cell and range names o cell addressing relative, absolute and mixed A1 relative $A$1 absolute A$1 relative column/absolute row $A1 absolute column/relative row fill a table with single formula result in single cell A1 $A1 F4 $A$1 note use of addressing copy to entire table A$1 use the F4 key to cycle through the addressing modes see how addressing translated to reference the appropriate cells Problem Solving for ChEs 7 creating formulas using cell and range names o creating names for cells and ranges of cells formula references cell addresses have to back-trace to cells to see meaning of formula references enter n in Name Box to create name n for cell B2 formula with names much easier to decipher (and debug) use names wherever possible! When not to use names? When you need to take advantage of cell addresses in copying formulas. Problem Solving for ChEs 8 4

5 creating formulas using cell and range names o introducing built-in functions (there are 100 s) use the Insert Function button just to the left of the Formula Bar to find and insert functions if we want to find out whether Excel has a built-in gamma function, type it in and click Go we find that Excel doesn t have the gamma function built in, but it does have the natural log of it so we can use EXP to convert that Problem Solving for ChEs 9 creating formulas using cell and range names o using array formulas one-stop shopping these ranges named V and T Array formulas also allow for matrix calculations (multiplication, inverse, transpose, determinant) select destination range and type in single formula making reference to V and T press Ctrl-Shift-Enter Problem Solving for ChEs 10 5

6 suggestions on creating engineering graphs o options with scatter plots avoid artificial smoothing options use markers only for experimental data use markers and straight lines for pattern recognition use straight lines only for analytical functions or hundreds of data o moving charts to their own sheet whenever feasible, move charts to their own sheet formatting and presentation is much better data avoid data avoid data scatter plots are the best choice for engineering graphs Problem Solving for ChEs 11 suggestions on creating engineering graphs o adding a data series to the graph many users don t realize that you can select a new data series on the spreadsheet, copy and paste it onto the chart, and it is added automatically o using a secondary y-axis if one or more series on the plot don t work well with the scale required on the left, assign them to a secondary scale on the right Series Series2 Series1 Series Problem Solving for ChEs

7 suggestions on creating engineering graphs o annotating graphs add text boxes, arrows pointing to features of the graph, shapes such as ellipses reformat these to suit 4.5 Heat Capacity of Nitric Acid Solutions Notice the inflection in the curve here kj/(kg*k) Heat Capacity ( %HNO 3 by wt 13 Problem Solving for ChEs case studies using Data Table Input cell Spreadsheet calculation involving one to many cells Result cell Set of input al es Corresponding result al es typically create graph of result vs input values values result Problem Solving for ChEs 14 7

8 case studies using Data Table o identifying the input cell(s) and output cell input cell output cell one-way case study o creating the range(s) of input values o entering the study formula Problem Solving for ChEs 15 case studies using Data Table o selecting the study range, invoking Data Table the Data Table is live -- change the temperature and the values will update notice the range selected includes F2 Problem Solving for ChEs 16 8

9 case studies using Data Table o graphical interpretation of the case study 2.5 Case Study of Ideal Gas Law Pressure versus Volume 2 Temperature = 32 degf Pressure (atm) Note: two-way case studies are possible and can be depicted in a surface or contour plot Volume (L) Problem Solving for ChEs 17 targeting calculations using Goal Seek o the back-solving scenario input cell adjust spreadsheet calculation l involving one or more cells Goal Seek output cell compare target value Problem Solving for ChEs 18 9

10 targeting calculations using Goal Seek o putting Goal Seek to work adjust V to get a pressure of 2 atm 2 Problem Solving for ChEs 19 targeting calculations using Goal Seek o using Goal Seek for equation solving f x 0 target value is zero o Solver as an alternative 2 Problem Solving for ChEs 20 10

11 optimizing with constraints using Solver o adjusting multiple cells to achieve an objective n input cells performance calculation performance result n 1 constraints t o constraint-free optimization n = 1 Problem Solving for ChEs 21 optimizing with constraints using Solver V V r h 2 cyl 1 1 r h 3 2 cone 2 Minimize total cost A 2 rh cyl 1 Cost cyl = $1000/m 2 Total Volume = 25 m Acone r r h2 Cost cone = $1500/m 2 Total Height = 5 m Three inputs: r, h 1 and h 2 Two constraints: total volume and total height One performance objective: total cost r h 1 h 2 Problem Solving for ChEs 22 11

12 optimizing with constraints using Solver Adjust h 1, h 2 and r to minimize TotalCost while keeping TotalHt = 5 and Volume = 25 Problem Solving for ChEs 23 optimizing with constraints using Solver o setting Solver parameters o adding constraints 24 Problem Solving for ChEs 12

13 optimizing with constraints using Solver Click Solve Optimized design Problem Solving for ChEs 25 o using Trendline its limitations and pitfalls to add a Trendline, right click a data point and click Add Trendline 26 Problem Solving for ChEs 13

14 o using Trendline its limitations and pitfalls Here, pick a polynomial fit and adjust the order until the fitted curve looks good. Check to display the model equation on the chart. We advise against displaying R 2, since it is a misleading statistic for goodness of fit. Problem Solving for ChEs 27 o using Trendline its limitations and pitfalls Visual fit appears good for 5 th order polynomial. Be cautious in manually copying model equation to use in calculations precision of display will cause (big!) round off errors. Statistical information on regression is not available. Flexibility in specifying model structure is very limited. Problem Solving for ChEs 28 14

15 o Data Analysis Regression allowable models Models must be linear in the parameters being fitted. Generally, y a f x,x,,x a f x,x,,x a f x,x,,x m m n n 1 2 m Example allowable linear models: n Polynomials: y a0 a1x anx Response surface: y a0 a1x1 a2x2 a12x1x2 (multilinear) Models nonlinear in parameters can t be handled: e.g., Antoine s Eqn B A T C PT 10 Problem Solving for ChEs 29 o step-wise regression using Data Analysis Create an array of the x variable (%HNO3) to powers 1 through 6 Set up the Regression dialog as shown Include Labels and Residuals Problem Solving for ChEs 30 15

16 o step-wise regression using Data Analysis From Regression output, find term with highest P value (2 nd order term) Run Regression again, eliminating the 2 nd order column from the X input range. Continue eliminating the highest P value until all are less than, for example, 5%. Notice result has intercept, first order, 4 th,5 th, and 6 th order not a conventional polynomial fit. This model would not have been found using Trendline. Problem Solving for ChEs 31 o step-wise regression using Data Analysis Heat Capacity of Nitric Acid Solutions Model curve E 02 Data shown with Model Residuals 1.5E 02 data and E 02 residuals plotted on 5.0E secondary 0.0E+00 axis E 03 Model equation embedded on 1.0E 02 10E graph using 1.5E 02 equation y x x x x E 02 typesetter Heat Capacity (kj/(kg*k) %HNO 3 by wt Residual Values Problem Solving for ChEs 32 16

17 o nonlinear regression use of Solver Start by creating a graph to test models Problem Solving for ChEs 33 o nonlinear regression use of Solver Choose an initial set of parameters and compute model predictions Add this curve to the graph Make sure the initial estimates are such that the model curve is in the ballpark of the data, as shown here. Problem Solving for ChEs 34 17

18 o nonlinear regression use of Solver Compute the differences between the predictions and data in the Error column sum the squares of this column in SSE Setup SolverParameters to minimize SSE by adjusting Antoine parameters. Problem Solving for ChEs 35 o nonlinear regression use of Solver Solver s minimization of SEE performs a nonlinear regression resulting in a snapping of the model curve onto the data. Problem Solving for ChEs 36 18

19 Problem Solving for ChEs Windup: A Few Key Points use names instead of cell addresses wherever possible take the time to learn efficient techniques try array formulas they improve reliability recognize the problem-solving scenarios we have left out many topics especially VBA Want to go more in depth on spreadsheets? Consider enrolling in the new on-line course Spreadsheet Problem Solving for ChEs to be offered by AIChE early next year or attend the AIChE/ASME 3-day short course Excel Programming/Spreadsheet Combo Thanks for your attention. Now, questions?? 37 19