This presentation was made at the NAFEMS European Conference on Simulation-Based Optimisation held on the 15th of October in London.
Optimisation has become a key ingredient in many engineering disciplines and has experienced rapid growth in recent years due to innovations in optimisation algorithms and techniques, coupled with developments in computer hardware and software capabilities. The growing popularity of optimisation in engineering applications is driven by ever-increasing competition pressure, where optimised products and processes can offer improved performance and cost-effectiveness which would not be possible using traditional design approaches. However, there are still many hurdles to be overcome before optimisation is used routinely for engineering applications.
The NAFEMS European Conference on Simulation-Based Optimisation brings together practitioners and academics from all relevant disciplines to share their knowledge and experience, and discuss problems and challenges, in order to facilitate further improvements in optimisation techniques.
Finite element (FE) models are typically used to understand the dynamic behavior of various components in an ASML chip manufacturing machine. The modal properties (eigen frequencies and mode shapes) provided by the FE model are not exactly the same as those collected via dynamic measurements. To update the FE model parameters, an optimisation problem is formulated to minimize the difference between experimental and simulated modal properties. Interface locations are typically modeled as springs with a certain interface stiffness which is taken as the design variable . The objective is defined as a function of the eigen frequencies and mode shapes and the Nelder Mead simplex algorithm is used to arrive at an optimal solution. The results of the original and optimised model are presented and compared with the experimental results.
Optimisation Process :
i) The optimisation problem consists in the minimization of an objective function related with the frequencies and respective mode shapes correlation between the model and measurements.
ii) The objective function incorporates the frequency delta and also if possible the MAC (Modal assurance criteria) values between the model and experiment
iii) The optimisation process uses the interaction between Ansys and MATLAB to improve the dynamic characteristics of the model by calculating the objective function value and finding the optimal value of the physical parameters. The work flow (Fig 1) consists of starting with an initial guess of the parameters, doing a modal analysis in ANSYS, exporting the results to MATLAB and performing the optimisation iteration and then re-solving the model in ANSYS with the updated parameters.
iv) It is possible to view and inspect the results of the optimisation, both while it is running and after if finishes.
Results and discussion
i) Results of relative difference between the original model and the optimised model with respect to experimental results are presented and compared. The figure below shows the typical improvement in the relative difference in the modal frequencies of the original and optimised model.
ii) A generalized method and automated workflow is aimed to be derived for simple FE models that can quickly be updated without spending too much time on setting up the optimisation problem.
iii) The efficiency of inbuilt functions of the MATLAB optimisation toolbox is demonstrated that can be utilized to setup and quite easily solve what would otherwise be quite a rigorous optimisation task.
|Date||15th October 2019|
|Organisation||ASML Netherlands B.V.|