Application of Engineering Models to Fit Experimental Data

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Application of Engineering Models to Fit
Experimental Data

• Lecture 2

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Extrapolate Data to Higher Temperatures and
Compare to Experimental Data
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Refine Model Using a 2nd Order Polynomial
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Extrapolate to Even Higher Temperatures
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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.

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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

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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?

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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.

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Linear Regression

• Go to Lecture2Example.xls

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This can be more than one column but they need to
be next to each other
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How to Calculate tobs
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Linear Regression with Multiple Independent
Variables

• Go to Lecture2Example.xls
• Sheet 2

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Non-Linear Equations

• How to turn non-linear equations into linear
  equations

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How do we get
To look like this
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In-Class Exercise
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Linearization of Non-Linear Equations

• Go to Lecture2Example.xls
• Sheet 3

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Review of Natural Logarithms
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Linearization of Equations
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Linearization of Non-Linear Equations

• Go to Lecture2Example.xls
• Sheet 4

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Using Solver to Determine Coefficients in
Non-Linear Equations
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Minimize Error Between Model Predictions and
Experimental Data