Skip to content

Curve Fitting

There are 8 types of functions available to the user to fit the data.

Example

Let us now make a curve fitting with the scatter plot from the previous section.

Make sure you have a scatter plot visible, then click on the Fitting tab to display the fitting pane:

curve-fitting-1.png curve-fitting-1-dark.png

Trace (Legend): the traces (legends) are automatically loaded as options, select a trace that you want to fit.

Fit equations: choose one of those equations below to fit.

  • 1st order: \(f(x) = A + Bx\)
  • 2nd order: \(f(x) = A + Bx + Cx^2\)
  • 3rd order: \(f(x) = A + Bx + Cx^2 + Dx^3\)
  • 4th order: \(f(x) = A + Bx + Cx^2 + Dx^3 + Ex^4\)
  • 5th order: \(f(x) = A + Bx + Cx^2 + Dx^3 + Ex^4 + Fx^5\)
  • 6th order: \(f(x) = A + Bx + Cx^2 + Dx^3 + Ex^4 + Fx^5 + Gx^6\)
  • Theil-Sen regression (robust 1st order): \(f(x) = A + Bx\) (Robust)
  • VFT: \(\log_{10}f(x) = A + B/(x - C)\)

Fit ranges (optional): the min/max x values are automatically set when trace is selected. You can manually modify the ranges later after fitting. Leave it blank to use the default values.

Initial guess (advanced): This option will be displayed when the VFT equation is selected. The initial guess values are set as 0 by default and will be updated automatically after fitting.

curve-fitting-5.png curve-fitting-5-dark.png

Note

The initial guess values are important for the VFT equation as we use fminsearch to fit the curve. If the fitting result is not good, you can tune the values to get a better result. You can also lock the values by clicking on the lock icon.

Fitting result: the fitting result (equation) or some messages are displayed here. You can copy the equation for use in other applications.

Again, let's use the trace Glass No: 20006 as an example, and since we already know that we are dealing with viscosity data, we choose the equation VFT for fitting.

curve-fitting-2.png curve-fitting-2-dark.png

Click on Curve fit to perform the fitting.

curve-fitting-3.png curve-fitting-3-dark.png

Show only the legend Glass No: 20006 and the legend Fit of Glass No: 20006: curve-fitting-4.png curve-fitting-4-dark.png

The fitted equation is: log₁₀f(x) = -0.937288 + 3466.14 / (x - 329.93)

You can estimate the viscosity at different temperatures by specifying the x ranges, e.g., set the max x range to 2000.

curve-fitting-6.png curve-fitting-6-dark.png

Info

We are also seeking for other good equations (models) like the Adam Gibbs equation to make better prediction (fitting). Please contact us if you know how or would like to help.