Study on Roundness Error Evaluation with Least-Squares Method Based on Nonlinear Optimization

Roundness error evaluation software is developed based on two-dimensional circle fitting with least-squares method based on nonlinear optimization with constraints. The local derivative-free optimization algorithms of NLopt can solve nonlinear constraint problems by combining with augmented Lagrangian algorithm. The fitting precision and convergence time of each algorithm are analyzed by calculating the fitting results with same test data to find its advantages and disadvantages. It is shown that each algorithm has different behaviors from others on performance and stability. This work provides a good basis for choosing the appropriate algorithm for roundness error evaluation.