MCalibration Tutorial: Convergence Properties for Different Optimization Methods

Goals of Study

MCalibration supports many different optimization methods. This study examines the performance of the different methods.

Overview

  • The different optimization methods are examined by studying 3 different test cases.
  • The optimization methods are applied, one at a time, to each test case with the same initial parameters.
  • The convergence properties are then extracted and compared.

Case 1: UHMWPE and BB-Model

This figure shows the experimental data and predictions from the initial set of material parameters. Different optimization methods are then examined using “Run Calibration”.

Here is the most accurate stress-strain prediction that was found.

The graph shows the fitness value as a function of the number of function evaluations. This shows the final low-fitness predictions in more detail.

 The following optimization algorithms reach the best fitness values: Automatic Extensive, NewUOA, Nelder-Mead (500/1000) and CMA-ES. The Automatic Extensive method converges the fastest, the CMA-ES method finds the best answer.

Case 2: UHMWPE and TNV-Model

This figure shows the predictions from the initial set of material parameters. Different optimization methods are then examined using “Run Calibration”.

Here is the most accurate stress-strain prediction that was found.

The graph shows the fitness value as a function of the number of function evaluations. This shows the final low-fitness predictions in more detail.

The following algorithms reach the global optimum: Quasi-Newton, Automatic Extensive and CMA-ES. The Automatic Extensive method gives the best results.

Case 3: Silicone Rubber and TNV Model

This figure shows the predictions from the initial set of material parameters. Different optimization methods are then examined using “Run Calibration”.

Here is the most accurate stress-strain prediction that was found.
Fitness value as a function of the number of function evaluations. This figure shows the final low-fitness predictions in more detail.

Summary

  • The Automatic Extensive and the CMA-ES optimization methods are most robust in finding the global optimal material parameters.
  • When using the Automatic Extensive method, selecting “Repeat the automatic optimization until no further improvements” often helps finding the optimal set of parameters.
  • The CMA-ES method often works better if realistic upper and lower bounds are specified for the material parameters.

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