An auto-didactic multivariable estimation scheme for a coupled map lattice: convergence analysis modeling of cylinder wakes

An auto-didactic (self-learning) coupled map lattice (CML) model for online estimation of wake patterns behind vibrating flexible cables in a fluid flow is developed. A spatio-temporal CML model, which combines a series of low-dimensional temporal circle maps with a convection-diffusion model, is used to predict qualitative features of cylinder wake patterns at low Reynolds number of the order of 100. However, due to the simple and computationally efficient nature of the CML models, there are always unmodelled dynamics if a quantitative comparison is made with wake patterns measured from a wake experiment or simulation. To overcome this limitation, self-learning features are incorporated into the basic CML model. The spanwise velocity distribution parameter in the self-learning CML is varied adaptively using a multivariable least squares algorithm in order to minimize the error between the actual and estimated wake patterns at every time-step. Proofs of convergence of the state and parameter errors to zero are presented. Studies of this approach are conducted for a NEKTAR (a highly accurate spectral element-based CFD solver) numerical experiment at Reynolds number = 100. It is observed that the proposed self-learning CML scheme efficiently predicts the NEKTAR wake patterns within several shedding cycles. Therefore, it is highly suitable for real-time estimation of experimental wake flows, as well as serving as a wake model in future anticipated flow control studies.