Nonlinear Multi-Time-Delay Stochastic Estimation: Application to Cavity Flow and Turbulent Channel Flow

A nonlinear extension of the multi-time-delay stochastic estimation technique is presented. The proposed approach consists of the design of nonlinear prediction filters based on artificial neural networks or, for smaller problems, on Volterra expansions of the measured wall variable. The application to two different flows is discussed. The first case is the estimation of the temporal dynamics of the velocity fluctuations in a cavity shear layer in low subsonic conditions from wall-pressure measurements. The second case is the estimation of the streamwise velocity fluctuations in the buffer layer of a fully developed turbulent channel flow from wall shear stress measurements. It is shown that the accuracy of the nonlinear technique is application dependent as it is significantly affected by the underlying nonlinear nature of the flow investigated. In particular, we show that, for the cavity shear layer case, the improvement is marginal and it does not appear to be worth the additional computational complexity associated with the nonlinear problem. On the other hand, the improvement in accuracy of the nonlinear estimation of the velocity fluctuations in the wall turbulence case is significant, owing to the strong nonlinearity of the dynamics in the wall-bounded flow.