63,740 research outputs found
Input-output analysis of stochastic base flow uncertainty
We adopt an input-output approach to analyze the effect of persistent
white-in-time structured stochastic base flow perturbations on the mean-square
properties of the linearized Navier-Stokes equations. Such base flow variations
enter the linearized dynamics as multiplicative sources of uncertainty that can
alter the stability of the linearized dynamics and their receptivity to
exogenous excitations. Our approach does not rely on costly stochastic
simulations or adjoint-based sensitivity analysis. We provide verifiable
conditions for mean-square stability and study the frequency response of the
flow subject to additive and multiplicative sources of uncertainty using the
solution to the generalized Lyapunov equation. For small-amplitude base flow
perturbations, we bypass the need to solve large generalized Lyapunov equations
by adopting a perturbation analysis. We use our framework to study the
destabilizing effects of stochastic base flow variations in transitional
parallel flows, and the reliability of numerically estimated mean velocity
profiles in turbulent channel flows. We uncover the Reynolds number scaling of
critically destabilizing perturbation variances and demonstrate how the
wall-normal shape of base flow modulations can influence the amplification of
various length scales. Furthermore, we explain the robust amplification of
streamwise streaks in the presence of streamwise base flow variations by
analyzing the dynamical structure of the governing equations as well as the
Reynolds number dependence of the energy spectrum.Comment: 29 pages, 21 figure
Identification of Stochastic Wiener Systems using Indirect Inference
We study identification of stochastic Wiener dynamic systems using so-called
indirect inference. The main idea is to first fit an auxiliary model to the
observed data and then in a second step, often by simulation, fit a more
structured model to the estimated auxiliary model. This two-step procedure can
be used when the direct maximum-likelihood estimate is difficult or intractable
to compute. One such example is the identification of stochastic Wiener
systems, i.e.,~linear dynamic systems with process noise where the output is
measured using a non-linear sensor with additive measurement noise. It is in
principle possible to evaluate the log-likelihood cost function using numerical
integration, but the corresponding optimization problem can be quite intricate.
This motivates studying consistent, but sub-optimal, identification methods for
stochastic Wiener systems. We will consider indirect inference using the best
linear approximation as an auxiliary model. We show that the key to obtain a
reliable estimate is to use uncertainty weighting when fitting the stochastic
Wiener model to the auxiliary model estimate. The main technical contribution
of this paper is the corresponding asymptotic variance analysis. A numerical
evaluation is presented based on a first-order finite impulse response system
with a cubic non-linearity, for which certain illustrative analytic properties
are derived.Comment: The 17th IFAC Symposium on System Identification, SYSID 2015,
Beijing, China, October 19-21, 201
- …