A nudged hybrid analysis and modeling approach for realtime wake-vortex transport and decay prediction

Abstract

In this paper, we put forth a long short-term memory (LSTM) nudging framework for the enhancement of reduced order models (ROMs) of fluid flows utilizing noisy measurements for air traffic improvements. Toward emerging applications of digital twins in aviation, the proposed approach allows for constructing a realtime predictive tool for wake-vortex transport and decay systems. We build on the fact that in realistic application, there are uncertainties in initial and boundary conditions, model parameters, as well as measurements. Moreover, conventional nonlinear ROMs based on Galerkin projection (GROMs) suffer from imperfection and solution instabilities, especially for advection-dominated flows with slow decay in the Kolmogorov width. In the presented LSTM nudging (LSTM-N) approach, we fuse forecasts from a combination of imperfect GROM and uncertain state estimates, with sparse Eulerian sensor measurements to provide more reliable predictions in a dynamical data assimilation framework. We illustrate our concept by solving a two-dimensional vorticity transport equation. We investigate the effects of measurements noise and state estimate uncertainty on the performance of the LSTM-N behavior. We also demonstrate that it can sufficiently handle different levels of temporal and spatial measurement sparsity, and offer a huge potential in developing next-generation digital twin technologies.

Hybrid deep-learning POD-based parametric reduced order model for flow around wind-turbine blade

“…To address these two hurdles, we propose a non-intrusive ROM (NIROM), which exploits the strengths of Long Short-Term Memory (LSTM) Recurrent Neural Networks (RNN) in accurately predicting time-series. The current work differs from the previous NIROM related works (e.g., [7,8,9,10]) in two regards. Firstly, it involves using a test case (NACA 0015 aerofoil) that consists of highly turbulent flow structures at high Reynolds number with complex physics.…”

Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolution

“…where is the forward model, +1 is the prior model prediction computed using imperfect background model, defined as +1 = ( ), is called the nudging (gain) matrix, is the set of measurements, and refers to the time index where we have these observations, while ℎ(⋅) is a mapping from model space to observation space. For example, ℎ(⋅) can be a reconstruction map, from ROM space to FOM space as shown in our recent studies [200,241] . In other words, ℎ( ) represents the "model forecast of the measured quantity", while is the "actual" observations.…”

“…Data-driven tools do an excellent job in terms of online time-cost, however, relying only on data and disregarding the known and well-established physics is not a wise step. Hybridization techniques have been demonstrated to give superior performance to either individual components [123,129,134,137,150,200] . Therefore, a DT based on HAM methodologies can be built to provide nature-informed indicators for near-time events.…”

Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolution

“…Data‐driven tools do an excellent job in terms of online time‐cost, however, relying only on data and disregarding the known and well‐established physics is not a wise step. Hybridization techniques have been demonstrated to give superior performance to either individual components [6,173,175,250,274,280]. Therefore, a DT based on HAM methodologies can be built to provide nature‐informed indicators for near‐time events.…”

“…In other words, the forward model given in Equation () is supplied with a nudging (or correction) term rewritten in the following discrete form, where is the forward model, is the prior model prediction computed using imperfect background model, defined as , G is called the nudging (gain) matrix, z is the set of measurements, and n refers to the time index where we have these observations, while h (·) is a mapping from model space to observation space. For example, h (·) can be a reconstruction map, from ROM space to FOM space as shown in our recent studies [6,8]. In other words, h ( u ) represents the “model forecast of the measured quantity,” while z is the “actual” observations.…”