9 March 2000
Sensitivity analysis for design and control in an elastic CAD-free framework for multi-model configurations
Dr Bijan Mohammadi
This lecture is about the extension of our CAD-Free platform to the simulation and sensitivity analysis for design and control of multi-model configurations. We present the different ingredients of the platform using simple models for the physic of the problem. This presentation enables for an easy evaluation of coupling, design and control strategies. \\ \\ Sensitivity analysis has been performed using automatic differentiation in direct or reverse modes and finite difference or complex variable methods. This former approach is interesting for cases where only one control parameter is involved as we can evaluate the state and sensitivity in real time with only one evaluation. \\ \\ We show that for some class of applications, incomplete sensitivities can be evaluated dropping the state dependency which leads to a drastic cost reduction. \\ \\ The design concerns the structural characteristic of the model and our control approach is based in perturbating the inflow incidence by a time dependent flap position described by a dynamic system encapsulating a gradient based minimization algorithm expressed as dynamic system. This approach enables for the definition of various control laws for different minimization algorithm. \\ \\ We present dynamic minimization algorithms based on the coupling of several heavy ball method. This approach enables for global minimization at a cost proportional to the number of balls times the cost of one steepest descent minimization. \\ \\ Two and three dimension flutter problem simulation and control are presented and the sensitivity of the different parameters in the model is discussed.
- Computational Mathematics and Applications Seminar