General perspectives on model construction and evaluation for stochastic estimation, with application to a blunt trailing edge wake

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

“…It is important to point out that the curve for the linear estimator, which shows the training error on the entire dataset, exhibits a rather flat plateau for large values of n, as opposed to what has been observed by other researchers, see for example references [7] and [3]. In these works, as the number of past samples in increased, the training error decreased monotonically, whereas the error on an independent validation set started to increase.…”

“…An interesting treatment of these issues in the context of flow state estimation is also given in the recent work of Clark et al, [3], where this issue is clearly demonstrated. For the two flows discussed in this paper, we have performed extensive preliminary tests for all the estimators presented.…”

“…Stochastic estimation techniques were made popular by the early works of Adrian [2], where it was used to approximate conditional averages for turbulent flows. Stochastic estimation has now matured to become an established research tool that is able to provide valuable insight into the dynamics of coherent structures in free and wall-bounded flows, see Clark et al [3] for recent perspectives on the topic.…”

Comparison of stochastic estimation methods with conditional events optimization for the reconstruction of the flow around a supercritical airfoil in transonic conditions

“…In 2014, Clark [19] stressed the direct link between SE and Linear Least Square Regression. He investigated the use of statistical tools such as the Variance Inflation Factor (VIF) in the case of MTD-LSE-POD estimation on a flow similar to the one of Tu and Durgesh.…”

“…In addition to the complex physics displayed by the flow, it involves a shock oscillation with a periodic flow separation and a vortex shedding downstream. Moreover, if the flow has a main oscillatory phenomenon (the shock wave oscillation) which is at low frequency, the oscillatory flow separation downstream the shock leads to a more complicated situation than blunt trailing edge wake flows mostly studied in recent works [10] [18] [19].…”