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L14 Curve Fitting

L14 Curve Fitting. Homework Curve Fitting – least squares Curve Fitting - optimization Summary. H13 prob 6.5. Beware: some problems don’t need solving! f ( x )=0, when x = 0!. H13 Prob 6.9. Prob 6.9 RJE sol’n. Prob 3.33. Why is this formulation better?. Prob 3.33 cont’d. Report #1.

denise-conway
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L14 Curve Fitting

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  1. L14 Curve Fitting • Homework • Curve Fitting – least squares • Curve Fitting - optimization • Summary

  2. H13 prob 6.5 Beware: some problems don’t need solving! f(x)=0, when x=0!

  3. H13 Prob 6.9

  4. Prob 6.9 RJE sol’n

  5. Prob 3.33 Why is this formulation better?

  6. Prob 3.33 cont’d

  7. Report #1

  8. Report #2

  9. Worksheet Modifications • Naming cells • Inserting shapes • Inserting MS Equation “object” • Recording macros • Attaching a macro to a shape • Creating a SOLVER hot button • Visual basic, tools/references/solver

  10. Figure 6.13 Excel worksheet for the spring design problem.

  11. Curve fitting

  12. Minimize sum of all errors?

  13. NC for Unconstrained z(a,b)

  14. Straight Line Least Squares All numbers Mathematical method that works for straight lines! Another way? Especially for non-linear curve fits?

  15. Types of curves Need to find the parameters ai Another way? Especially for non-linear curve fits?

  16. Use Excel & Solver (Garnero)?

  17. Curve Fit example

  18. Summary • Pay attention to layout • Design variables • Parameters • Analysis/Performance “Variables” • Objective function • Constraints • May need multiple starting points • Curve fitting w/optimization methods = min sum of errors to find parameters ai

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