Least Squares Shadowing sensitivity analysis of chaotic limit cycle oscillations
Author(s)Wang, Qiqi; Hu, Rui; Blonigan, Patrick Joseph
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The adjoint method, among other sensitivity analysis methods, can fail in chaotic dynamical systems. The result from these methods can be too large, often by orders of magnitude, when the result is the derivative of a long time averaged quantity. This failure is known to be caused by ill-conditioned initial value problems. This paper overcomes this failure by replacing the initial value problem with the well-conditioned “least squares shadowing (LSS) problem”. The LSS problem is then linearized in our sensitivity analysis algorithm, which computes a derivative that converges to the derivative of the infinitely long time average. We demonstrate our algorithm in several dynamical systems exhibiting both periodic and chaotic oscillations.
DepartmentMassachusetts Institute of Technology. Department of Aeronautics and Astronautics
Journal of Computational Physics
Wang, Qiqi, Rui Hu, and Patrick Blonigan. “Least Squares Shadowing Sensitivity Analysis of Chaotic Limit Cycle Oscillations.” Journal of Computational Physics 267 (June 2014): 210–224.