Neural Network-Based Model Reduction of Hydrodynamics Forces on an Airfoil

Farooq, Hamayun; Saeed, Ahmad; Akhtar, Imran; Bangash, Zafar

doi:10.3390/fluids6090332

Cited by 11 publications

(6 citation statements)

References 68 publications

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“…It also indicates that the first four modes carry

of the total energy. Unlike the circular cylinder [ 70 ] and static airfoils at different angles of attack [ 32 ], where pressure modes are either pairwise symmetric or antisymmetric, the modes in the case of flapping airfoil corresponding to the power generation regime do not exhibit pairwise symmetry or antisymmetry. It is observed that after a symmetric mode about the center line (

), there is a pair of antisymmetric modes.…”

Section: Resultsmentioning

confidence: 99%

“…The fractional step method is an effective and strong candidate technique for dealing with incompressible Navier-Stokes equation. It transforms the momentum equation into the convection-diffusion equation and pressure-Poisson equation [32,40,51,66]. We utilize a non-staggered grid in which the velocity and pressure fields are computed at the center of each cell.…”

Section: Discretization Strategymentioning

confidence: 99%

“…Recently, Ahmed et al [ 31 ] used PMD technique to develop an ML-based ROM to predict the lift and drag forces for flows around circular cylinders. Later, Farooq et al [ 32 ] developed an ANN-based ROM to approximate the hydrodynamic forces on a NACA-0012 airfoil exerted by the fluid flows, passing over it at different angles-of-attack (AoA). The trained model produced accurate values of lift and drag forces that match well with the true values obtained through direct numerical simulations.…”

Section: Introductionmentioning

confidence: 99%

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Deep-Learning-Based Reduced-Order Model for Power Generation Capacity of Flapping Foils

et al. 2023

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Inspired by nature, oscillating foils offer viable options as alternate energy resources to harness energy from wind and water. Here, we propose a proper orthogonal decomposition (POD)-based reduced-order model (ROM) of power generation by flapping airfoils in conjunction with deep neural networks. Numerical simulations are performed for incompressible flow past a flapping NACA-0012 airfoil at a Reynolds number of 1100 using the Arbitrary Lagrangian–Eulerian approach. The snapshots of the pressure field around the flapping foil are then utilized to construct the pressure POD modes of each case, which serve as the reduced basis to span the solution space. The novelty of the current research relates to the identification, development, and employment of long-short-term neural network (LSTM) models to predict temporal coefficients of the pressure modes. These coefficients, in turn, are used to reconstruct hydrodynamic forces and moment, leading to computations of power. The proposed model takes the known temporal coefficients as inputs and predicts the future temporal coefficients followed by previously estimated temporal coefficients, very similar to traditional ROM. Through the new trained model, we can predict the temporal coefficients for a long time duration that can be far beyond the training time intervals more accurately. It may not be attained by traditional ROMs that lead to erroneous results. Consequently, the flow physics including the forces and moment exerted by fluids can be reconstructed accurately using POD modes as the basis set.

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“…It also indicates that the first four modes carry

), there is a pair of antisymmetric modes.…”

Section: Resultsmentioning

confidence: 99%

Section: Discretization Strategymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Deep-Learning-Based Reduced-Order Model for Power Generation Capacity of Flapping Foils

et al. 2023

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“…Recently, Ahmed et al (2021) developed an ANN-based ROM (ANN-ROM) solver to predict the lift and drag forces for a flow around a circular cylinder. Later, Farooq et al (2021) developed an ANN-ROM to approximate the hydrodynamic forces on NACA-0012 airfoil immersed in a flow field at different angles of attack. The trained model gives accurate values of lift and drag forces compared to true values obtained from direct numerical simulations.…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Reduced-Order Modeling of Blood Flow in a Constricted Channel with Magnetic Field Effect using Deep Learning

Farooq,

Ali,

Umar

et al. 2023

Preprint

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In an era characterized by an unprecedented influx of data across various domains, the quest for efficient, accurate, and computationally feasible modeling or reduced-order modeling (ROM) techniques has become paramount. This paper embarks on an exploration of leveraging the power of artificial neural networks (ANNs) as a data-driven approach to constructing ROM for non-Newtonian blood flows with magnetic field effects in an artery with plaque (a two-dimensional channel with uniform constriction). Several highdimensional simulations are performed in the parametric space of the Reynolds number and Hartmann number to generate the dataset for the training of the deep-learning model. The parametric space constitutes a wide range of Reynolds numbers from 1.0×102 to 1.1×103 and Hartmann numbers from 0 to 30. The snapshots of the vorticity field have been utilized to construct the proper-orthogonal decomposition (POD) to reconstruct the data-driven lowdimensional version of vorticity. In the ANN model, the past-time temporal coefficients along with the case value of the Reynolds number and Hartmann number used as the input to predict the future-time temporal coefficients following through the deep neural networks. These coefficients, in turn, are used to reconstruct the vorticity in a Galerkin fashion. The accuracy of the trained ANN model is tested by predicting the coefficients of several unseen cases, those which were not used in the training process. Results show remarkable predictive accuracy of the trained model. Thus, the ANN-based ROM (ANN-ROM) can be used as a real-time device in the field of biomechanical engineering to accurately predict the flow field and shear stresses on the artery surfaces.

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“…In the era of big data, numerous science and engineering disciplines use dimensionality reduction to obtain lower-dimensional representations of complex physical systems with many degrees of freedom [1][2][3][4][5][6][7][8] . Large data coming from system measurements or simulations is frequently the starting point of reduced-order modeling.…”

mentioning

confidence: 99%

Cost function for low-dimensional manifold topology assessment

Zdybał

Armstrong

Sutherland

et al. 2022

Sci Rep

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In reduced-order modeling, complex systems that exhibit high state-space dimensionality are described and evolved using a small number of parameters. These parameters can be obtained in a data-driven way, where a high-dimensional dataset is projected onto a lower-dimensional basis. A complex system is then restricted to states on a low-dimensional manifold where it can be efficiently modeled. While this approach brings computational benefits, obtaining a good quality of the manifold topology becomes a crucial aspect when models, such as nonlinear regression, are built on top of the manifold. Here, we present a quantitative metric for characterizing manifold topologies. Our metric pays attention to non-uniqueness and spatial gradients in physical quantities of interest, and can be applied to manifolds of arbitrary dimensionality. Using the metric as a cost function in optimization algorithms, we show that optimized low-dimensional projections can be found. We delineate a few applications of the cost function to datasets representing argon plasma, reacting flows and atmospheric pollutant dispersion. We demonstrate how the cost function can assess various dimensionality reduction and manifold learning techniques as well as data preprocessing strategies in their capacity to yield quality low-dimensional projections. We show that improved manifold topologies can facilitate building nonlinear regression models.

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Neural Network-Based Model Reduction of Hydrodynamics Forces on an Airfoil

Cited by 11 publications

References 68 publications

Deep-Learning-Based Reduced-Order Model for Power Generation Capacity of Flapping Foils

Deep-Learning-Based Reduced-Order Model for Power Generation Capacity of Flapping Foils

Data-Driven Reduced-Order Modeling of Blood Flow in a Constricted Channel with Magnetic Field Effect using Deep Learning

Cost function for low-dimensional manifold topology assessment

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