Simplify the Optimization Problem

Simplify the calibration problem by specifying the convergence criteria and bounds for the solution.

Like any iterative simulation, each iteration in a material calibration has a computational cost. Each additional iteration can offer diminishing returns. In this section, you can reduce this cost by specifying convergence criteria that control the optimization in these ways:

  • By defining a minimum error function decrease below which the calibration ends.
  • By defining the minimum allowable changes in parameters below which the calibration ends.
  • By specifying the maximum number of iterations for which the problem can run or the total number of optimization function evaluations.

  1. From the Optimization Controls panel, confirm that the Solution tolerance is 1E-06 and that the Function tolerance is 2.22E-12.

    The solution tolerance and function tolerance values determine the convergence criterion; that is, they determine whether the changes between iterations are small enough that the problem has converged to a solution. The solution tolerance specifies the tolerance for changes to calibrated parameters, while the function tolerance specifies the tolerance for the decrease to the objective function value.

  2. Confirm that the Maximum function evaluations and Maximum number of iterations are both equal to 10000.

    Placing limits on the number of function evaluations and the number of iterations can help you end calibrations that are not converging to a solution quickly enough. This calibration should complete long before 10000 function evaluations or iterations, so these limits are appropriate for this example.

  3. Select Compute parameter sensitivities if it is not already selected.

    A parameter's sensitivity indicates how much influence the parameter has on the calibrated response. You adjust selected sensitivity values in the next topic.

  4. Click Close.
  5. From the Calibration setup dialog box, ensure that the minimum C10 value in the Hyperelastic tab is 0 and set maximum and minimum bounds for each initialized hyperelastic parameter.

    Derivative-free algorithms like Nelder-Mead do not require maxima and minima to converge on a solution. However, specifying these values can improve efficiency and help you avoid local maxima and minima in the calibration.