MCalibration Parameter Connections

Introduction

There are different ways to impose constraints or connections between parameters in MCalibration. In the window below, the parameters mu and tauBase are unknown and will be search for during a calibration. There is no connection between the two parameters.

Parameter Constraint Option 1

Note that if two parameters in the Optimize column have the same (non-zero) value then those two parameters will be forced to have the same value. That value will be searched for during an optimization. This is my preferred method to impose a constraint between two parameters. It is very easy to use, and usually good enough.

Parameter Constraint Option 2

One way to impose a constraint on the value of a parameter is to set its lower and upper bound based on the value of other parameters. In this example, the parameter tauBase has a lower bound that is 1.9 times mu, and an upper bound that is 2.1 times mu. Both parameters are independent, but the tauBase parameter has to be within the bounds specified by mu. Note that this constraint option does not always work so well, and is my least favorite of the 4 options summarized here.

Parameter Constrains Option 3

Another way to impose a connection between different parameters is to use the Fitness dialog (button with the text “Fit”). In this way you can add a fitness penalty factor based on the value of the current material parameter set. In a sense this is similar to a Lagrange multiplier. In the example below, MCalibration will try to find parameters such that (tauBase-2*mu) becomes close to zero, in orther words, tauBase gets a value that is 2.0 times mu. The pre-factor 10, in the example, specifies how important this constraint is. 

Parameter Constraint Option 4

A fourth and final way to impose constraints between parameters is to write them in the material model dialog as part of a material model template. In the example below, the PolyUMod BB model template has been modified so that instead of defining the parameter %tauBase%, it uses the equation $2.2*mu$. This will completely eliminate the tauBase parameter since it is instead fully defined by the other parameters.

Once you accept the modified material model, the main window of MCalibration looks as follows:

In this case the parameter tauBase is not part of the table of parameters. It is instead directly defined by the template we just edited.w

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