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Application of Engineering Models to Fit Experimental Data

Application of Engineering Models to Fit Experimental Data. Lecture 1. Extrapolate Data to Higher Temperatures and Compare to Experimental Data. Refine Model Using a 2 nd Order Polynomial. Extrapolate to Even Higher Temperatures. Conclusions.

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Application of Engineering Models to Fit Experimental Data

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  1. Application of Engineering Models to Fit Experimental Data Lecture 1

  2. Extrapolate Data to Higher Temperatures and Compare to Experimental Data

  3. Refine Model Using a 2nd Order Polynomial

  4. Extrapolate to Even Higher Temperatures

  5. Conclusions • Trendline models are not to be extrapolated beyond the range of data that they were derived. • All models are wrong, but some are useful.

  6. As Engineers, How do we properly model data? • Apply models based on physical principles • Test our models using statistical principles • Refine our models if there is disagreement with data • If the model does not fit the data, throw out the model, not the data

  7. The Power of the Linear Model y = mx + b • Does the model fit the data, or should a different model be used? • Are the values of m and b significantly different from zero? • Are the values of m and b significantly different from values obtained in a different experiment?

  8. Before Applying Models to Data …. • Graph the data to see if a linear model will produce a good fit or it the data exhibit curvature. • See if there is excessive scatter in the data. Other variables may influence the results that are not accounted for. • Test the results with statistics to determine if coefficients can be dropped out of the model.

  9. Linear Regression Go to Lecture1Example.xls

  10. This can be more than one column but they need to be next to each other

  11. Probability that the model fit the data by chance alone Values of b and m Standard Errors of b and m tobs when comparing b and m to zero a risk for stating b and m are not zero Lower and upper confidence intervals for b and m

  12. Linear Regression with Multiple Independent Variables Go to Lecture1Example.xls Sheet 2

  13. Non-Linear Equations How to turn non-linear equations into linear equations

  14. How do we get To look like this:

  15. In-Class Exercise

  16. Linearization of Non-Linear Equations Go to Lecture1Example.xls Sheet 3

  17. Review of Natural Logarithms

  18. Linearization of Equations

  19. Linearization of Non-Linear Equations Go to Lecture1Example.xls Sheet 4

  20. Using Solver to Determine Coefficients in Non-Linear Equations

  21. Minimize Error Between Model Predictions and Experimental Data

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