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Statistics and Probability: Betting on a Design

Statistics and Probability: Betting on a Design. Introduction to Engineering Systems Lecture 5 (9/11/2009). Prof. Andrés Tovar. Announcements. SAP2000 (Windows only) is now available on CD in the Engineering Library Avoid printing in the Learning Center, especially class handouts!.

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Statistics and Probability: Betting on a Design

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  1. Statistics and Probability:Betting on a Design Introduction to Engineering Systems Lecture 5 (9/11/2009) Prof. Andrés Tovar

  2. Announcements • SAP2000 (Windows only) is now available on CD in the Engineering Library • Avoid printing in the Learning Center, especially class handouts! Betting on a Design

  3. Betting on a Tower Design key idea • Use SAP2000 (theoretical model) together with experimental data (empirical model) • to design a bracing scheme that is safe (limited displacement) • but that is still cost efficient • Where should we aim? • But the real world isn’t ideal SAP2000 • SAP2000 simulates ideal tower behavior • see the effects of changing the bracing without having to build it. Betting on a Design

  4. Empirical model % The launcher X = (0.25:0.25:1.5)'; D = [1;4;10;18;27;36]; % linear prediction c = polyfit(X,D,1); Dc = polyval(c,X); % cuadratic prediction d = polyfit(X,D,2); Dd = polyval(d,X); plot(X,D,'ro-',X,Dc,'b-',X,Dd,'k--') xlabel('horizontal pullback X (m)') ylabel('distance D (m)') title('the launcher') Predictions depend on the basis function of the model. piecewise-linear model (ro-) linear model (b-) quadratic model (k--) Betting on a Design

  5. Firing at a Target X D Adjust the pullback distance X of the slingshot to hit a target at a distance D downrange. The bet: can you come within 1 m of a target at a distance D = 18 m? Betting on a Design

  6. How consistent is the launcher? Suppose that on Monday you determined an optimal value for X (from experimentation) to launch a ball 18 m On Tuesday, you ran 20 trials at that same setting for X and got the following results: Betting on a Design

  7. Review: Model Inputs and Outputs • Design variables (input, independent) • pullback X • Environmental variables • wind velocity (speed and direction) • temperature • name some more… • Behavioral variables (output, dependent) • distance D Betting on a Design

  8. Sources of Uncertainty in a Model • Uncertainty can be • Epistemic • lack of knowledge • Aleatory • random events Betting on a Design

  9. Scatterplot of Trials Betting on a Design

  10. Arithmetic Mean In Matlab see function mean. Out of curiosity you can check median and mode. Usually just called the “mean” (but there are other kinds of means) What is usually meant when we say “average” (but there are other kinds of averages) Betting on a Design

  11. Mean and Error About the Mean Betting on a Design

  12. Standard Deviation In this Class: typo in equation (5.4) = 1.4 m In Matlab see function std - 1 Square root of . . . the average of the squares of the errors Betting on a Design

  13. Coefficient of Variation Standard deviation divided by the mean Normalized version of the standard deviation Betting on a Design

  14. Systematic and Random Error Why did I miss the target? target • Systematic error • error between the mean of the trials and the target • Random error • random error of trials about the mean Betting on a Design

  15. Causes of Systematic and Error How many can you think of? • Systematic error • Wind between two days • Temperature • Settings, e.g., angles, references • Random error • Wind while the softball is flying • Grip of the softball • Distractions Betting on a Design

  16. Back to the Tower Hooke’s Law k = stiffness coefficient Displacement Scatter plot Betting on a Design

  17. Displacement statistics   – Betting on a Design

  18. Best-Fit Tower Force-Displacement Lines Betting on a Design

  19. Stiffness statistics  m – m = 0.07 N/mm s = 0.02 N/mm Betting on a Design

  20. Understanding Excel Spreadsheet of Test Results (A typical section tab) Results from yellow test fixture. Dial gauge measurements from Section 1 Red test fixture. Applied Forces Measurement after initial displacement is subtracted. Stiffness as computed by Excel Function (includes stiffness of dial gauge). Corrected Tower stiffness (after removal of dial gauge)

  21. The Summary Tab of the Excel Spreadsheet The mean and standard deviation of the entries in the Summary Table Table containing tower stiffness values for each tower tested in Learning Center 1 (ktower from Section tabs)

  22. How to determine an equivalent stiffness? Springs in series http://www.csun.edu/~ehrgott/EXP6.pdf Betting on a Design

  23. How to determine an equivalent stiffness? Springs in parallel http://www.csun.edu/~ehrgott/EXP6.pdf Betting on a Design

  24. Background / Usage: Mixed usage. Urban setting with the first 2 floors designated as parking garage so no interior bracing on those floors. The top 3 floors are for a hotel, with the top most floor (floor 5) being the penthouse so no bracing of any kind on that floor. Floors 3 & 4 cannot have any exterior diagonals. Team 1 Penthouse of Hotel Floor 5 Floor 4 Hotel Limit State (under 4.5N load): 5 mm Hotel Floor 3 Parking Floor 2 Floor 1 Parking Note: No bracing on a floor still Allows the addition of the center Plane vertical members http://farm4.static.flickr.com/3076/2764309768_e84db7fd77.jpg

  25. Background / Usage: Mixed usage. Located near a college campus, the first 3 floors are student apartments (any bracing scheme is permitted). The top 2 floors are high end loft style condominiums that require wide open spacing and unobstructed views (no bracing is permitted). Team 2 Condo Floor 5 Condo Floor 4 Limit State (under 4.5N load): 19 mm Apt. Floor 3 Example: Eddy Street Commons – South Bend, IN Apt. Floor 2 Floor 1 Apt. Note: No bracing on a floor still Allows the addition of the center Plane vertical members http://newsinfo.nd.edu/assets/7534/eddy_street_release.jpg

  26. Background / Usage: Mixed usage. Urban setting with the bottom floor being reserved for store front, the user of which has not been determined. In order to maximize flexibility no diagonal bracing is permitted on exterior of the first floor. The middle 3 floors are financial office suites, any bracing is permitted. Finally the top floor is for a Steakhouse, so no exterior bracing of any kind on that floor. Team 3 Restaurant Floor 5 Office Floor 4 Limit State (under 4.5N load): 7 mm Office Floor 3 Office Floor 2 Store Front Floor 1 http://www.anaheimoc.org/client_upload/images/ruth_schrisdining.JPG

  27. Background / Usage: Mixed usage. The bottom 2 floors are being used by Dave & Busters, and will not allow any interior bracing. The top 3 floors are office space, with the CEO’s offices taking up the middle floor. In order to have flexibility for unobstructed views of the city, there is no exterior bracing permitted on the middle floor. Team 4 Office Floor 5 Office Floor 4 CEO Office Limit State (under 4.5N load): 5 mm Floor 3 Dave & Busters Floor 2 Dave & Busters Floor 1 Note: No bracing on a floor still Allows the addition of the center Plane vertical members www.twincitiesrestaurantblog.com/tcrb/images/

  28. Background / Usage: Mixed usage. The bottom 2 floors are for a theater – they have very few exterior windows so exterior bracing is permitted but no interior bracing. The hotel requires no exterior diagonal bracing (any other form is permitted) Team 5 Hotel Floor 5 Hotel Floor 4 Limit State (under 4.5N load): 10 mm Hotel Floor 3 Theater Floor 2 Floor 1 Theater http://media.timeoutchicago.com/resizeImage/htdocs/export_images/161/161.feat.mock.wicked.V.jpg?

  29. Background / Usage: This building is for IKEA. The first floor does not allow any bracing so store front windows would be unobstructed and there are open areas for displays. Likewise, the top 4 floors are not permitted to have any interior diagonal bracing (any form of exterior bracing is permitted). Team 6 IKEA Floor 5 IKEA Floor 4 Limit State (under 4.5N load): 8 mm IKEA Floor 3 IKEA Floor 2 IKEA Store Front Floor 1 Note: No bracing on a floor still Allows the addition of the center Plane vertical members http://www.e-clipsblog.co.uk/wp-content/ikea.jpg

  30. Background / Usage: This building is a hospital. All floors require minimum obstructions for easy maneuvering & observation, so no interior bracing is allowed. The first floor is for outpatients and is the location of the emergency room- this requires easy access, so no diagonal bracing is allowed on this floor. All other floors allow any exterior bracing scheme. Limit State (under 4.5 N load): 4 mm Team 7 Hospital Floor 5 Hospital Floor 4 Hospital Floor 3 Hospital Floor 2 Outpatient & ER Floor 1 http://www.mc.uky.edu/OBG/Images/Tour/Campus/new_hospital1.JPG

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