CNN-SINDy Based Reduced Order Modeling of Unsteady Flow Fields

2019 ◽  
Author(s):  
Takaaki Murata ◽  
Kai Fukami ◽  
Koji Fukagata
Keyword(s):  
Temporal Evolution ◽  
Flow Fields ◽  
Cylinder Wake ◽  
Order Model ◽  
Reduced Order ◽  
Energy Reconstruction ◽  
Low Dimensional ◽  
Proper Orthogonal ◽  
Reconstruction Rate ◽  
New Framework

Abstract We present a new framework of nonlinear reduced order model to extract low-dimensional modes and to predict their temporal evolutions. Autoencoder-type Convolutional Neural Network (CNN) which can learn nonlinearity of data is used to extract low-dimensional modes. For obtaining the temporal evolution of a mapped data by CNN, Sparse Identification of Nonlinear Dynamics (SINDy) is performed. The proposed method is applied to a circular cylinder wake at ReD = 100. The CNN trained using fluctuation components of velocity vector u, v shows better results than the snapshot Proper Orthogonal Decomposition in terms of the energy reconstruction rate. Although time-evolving flow fields reproduced by SINDy equation also show reasonable agreement with the reference direct numerical simulation, the errors of CNN and SINDy are accumulated through integral computation. The error of CNN can be reduced by devising a better network structure; however, the error of SINDy depends on the waveform of latent vector.

Data-Driven Reduced Order Modeling of Flows Around Two-Dimensional Bluff Bodies of Various Shapes

2019 ◽  
Author(s):  
Kazuto Hasegawa ◽  
Kai Fukami ◽  
Takaaki Murata ◽  
Koji Fukagata
Keyword(s):  
Number Fields ◽  
Flow Fields ◽  
Reduced Order Modeling ◽  
Reduced Order Model ◽  
Data Driven ◽  
Bluff Bodies ◽  
Two Dimensional ◽  
Order Model ◽  
Reduced Order ◽  
Low Dimensional

Abstract We propose a reduced order model for predicting unsteady flows using a data-driven method. As preliminary tests, we use two-dimensional unsteady flow around bluff bodies with different shapes as the training datasets obtained by direct numerical simulation (DNS). Our machine-learned architecture consists of two parts: Convolutional Neural Network-based AutoEncoder (CNN-AE) and Long Short Term Memory (LSTM), respectively. First, CNN-AE is used to map into a low-dimensional space from the flow field data. Then, LSTM is employed to predict the temporal evolution of the low-dimensional data generated by CNN-AE. Proposed machine-learned reduced order model is applied to two-dimensional circular cylinder flows at various Reynolds numbers and flows around bluff bodies of various shapes. The flow fields reconstructed by the machine-learned architecture show reasonable agreement with the reference DNS data. Furthermore, it can be seen that our machine-learned reduced order model can successfully map the high-dimensional flow data into low-dimensional field and predict the flow fields against unknown Reynolds number fields and shapes of bluff body. As concluding remarks, we discuss the extension study of machine-learned reduced order modeling for various applications in experimental and computational fluid dynamics.

Reduced-Order Model of a Bladed Rotor With Geometric Mistuning

2007 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Coordinate Measurement ◽  
Coordinate Measurement Machine ◽  
Bladed Disk ◽  
Bladed Rotor ◽  
Proper Orthogonal

This paper deals with the development of an accurate reduced-order model of a bladed disk with geometric mistuning. The method is based on vibratory modes of various tuned systems and proper orthogonal decomposition of coordinate measurement machine (CMM) data on blade geometries. Results for an academic rotor are presented to establish the validity of the technique.

scholarly journals Local improvements to reduced-order models using sensitivity analysis of the proper orthogonal decomposition

2009 ◽  
Vol 629 ◽  
pp. 41-72 ◽  
Author(s):  
ALEXANDER HAY ◽  
JEFFREY T. BORGGAARD ◽  
DOMINIQUE PELLETIER
Keyword(s):  
Sensitivity Analysis ◽  
Proper Orthogonal Decomposition ◽  
Stokes Equations ◽  
Orthogonal Decomposition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Reduced Order ◽  
Selection Step ◽  
Low Dimensional ◽  
Proper Orthogonal

The proper orthogonal decomposition (POD) is the prevailing method for basis generation in the model reduction of fluids. A serious limitation of this method, however, is that it is empirical. In other words, this basis accurately represents the flow data used to generate it, but may not be accurate when applied ‘off-design’. Thus, the reduced-order model may lose accuracy for flow parameters (e.g. Reynolds number, initial or boundary conditions and forcing parameters) different from those used to generate the POD basis and generally does. This paper investigates the use of sensitivity analysis in the basis selection step to partially address this limitation. We examine two strategies that use the sensitivity of the POD modes with respect to the problem parameters. Numerical experiments performed on the flow past a square cylinder over a range of Reynolds numbers demonstrate the effectiveness of these strategies. The newly derived bases allow for a more accurate representation of the flows when exploring the parameter space. Expanding the POD basis built at one state with its sensitivity leads to low-dimensional dynamical systems having attractors that approximate fairly well the attractor of the full-order Navier–Stokes equations for large parameter changes.

scholarly journals Reduced-Order Modeling Based on Hybrid Snapshot Simulation

2020 ◽  
Vol 18 (01) ◽  
pp. 2050029 ◽  
Author(s):  
Feng Bai ◽  
Yi Wang
Keyword(s):  
Quality Data ◽  
Data Generation ◽  
Order Model ◽  
High Quality Data ◽  
Reduced Order ◽  
Online Simulation ◽  
Data Fidelity ◽  
Value Decomposition ◽  
Proper Orthogonal ◽  
Traditional Counterpart

This paper presents a hybrid snapshot simulation methodology to accelerate the generation of high-quality data for proper orthogonal decomposition (POD) and reduced-order model (ROM) development. The entire span of the snapshot simulation is divided into multiple intervals, each simulated by either high-fidelity full-order model (FOM) or fast local ROM. The simulation then alternates between FOM and local ROM to accelerate snapshot data generation while maintaining the data fidelity and representation. Model switch is determined on-the-fly by evaluating several criteria that monitor the dominance of leading POD modes and ROM trajectory. The incremental singular value decomposition (iSVD) is employed to continuously update ROMs for enhanced accuracy and utilization. A global ROM broadly applicable to various online simulation is immediately available at the end of the simulation. The hybrid snapshot simulation demonstrates excellent accuracy ([Formula: see text] error) and 2.09–2.6[Formula: see text]X speedup relative to its traditional counterpart. The constructed ROMs also preserve salient accuracy ([Formula: see text] error). The results prove feasibility of the proposed method for robust and efficient snapshot data generation and ROM development.

Temporal evolution analysis of in-cylinder flow by means of proper orthogonal decomposition

2020 ◽  
pp. 146808742091724
Author(s):  
Li Shen ◽  
Kwee-Yan Teh ◽  
Penghui Ge ◽  
Fengnian Zhao ◽  
David LS Hung
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Internal Combustion Engines ◽  
Temporal Evolution ◽  
Flow Fields ◽  
Orthogonal Decomposition ◽  
Temporal Behavior ◽  
Decomposition Approach ◽  
Cylinder Flow ◽  
Proper Orthogonal ◽  
Low Order

In-cylinder flow fields and their temporal evolution have strong effect on the combustion dynamics of internal combustion engines. Proper orthogonal decomposition is a statistical tool to analyze these flow fields by decomposing them into flow patterns (known as proper orthogonal decomposition modes) and corresponding coefficients with their contribution to the ensemble flow kinetic energy successively maximized. However, neither of the two prevailing proper orthogonal decomposition approaches satisfactorily describes the temporal behavior of the flow fields. The phase-dependent proper orthogonal decomposition approach is limited to analyzing spatial flow structures at a certain engine phase. The phase-invariant proper orthogonal decomposition approach attempts to account for both spatial and temporal variations, but at the expense of diminished statistical and physical significance. In this article, we seek to understand the temporal behavior of tumble flow fields by analyzing the evolution of low-order phase-dependent proper orthogonal decomposition modes over multiple crank angles. The concept of relevance index is first generalized to enable comparison between two vectorial fields of different sizes. This metric is then used to quantify the directional similarities between the two lowest proper orthogonal decomposition modes obtained at sequential crank angles. The mode shapes are observed to evolve gradually and naturally over most crank angles, but change significantly at certain crank angles during intake. The results indicate that each of the low-order modes features strong velocity fluctuations in different regions of the tumble plane, and different numbers of modes are needed to represent the dominant features of tumble flow at different engine phases. Based on this understanding, we propose to use the partial sum of those proper orthogonal decomposition modes and their coefficients to form a low-order approximation model of the in-cylinder tumble flow, in order to reduce flow field complexity and noise while retaining its major spatial and temporal features.

Reduced-Order Model of Unsteady Flows in a Turbomachinery Fan Modeled Using a Novel Proper Orthogonal Decomposition

2019 ◽  
Author(s):  
Elizabeth H. Krath ◽  
Forrest L. Carpenter ◽  
Paul G. A. Cizmas ◽  
David A. Johnston
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Reference Conditions ◽  
Stable Solution ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Computational Time ◽  
Order Model ◽  
Reduced Order ◽  
Proper Orthogonal ◽  
Model Rotor

Abstract This paper presents a novel, more efficient reduced-order model based on the proper orthogonal decomposition (POD) for the prediction of flows in turbomachinery. To further reduce the computational time, the governing equations were written as a function of specific volume instead of density. This allowed for the pre-computation of the coefficients of the system of ordinary differential equations that describe the reduced-order model. A penalty method was developed to implement time-dependent boundary conditions and achieve a stable solution for the reduced-order model. Rotor 67 was used as a validation case for the reduced-order model, which was tested for both on- and off-reference conditions. This reduced-order model was shown to be more than 10,000 times faster than the full-order model.

scholarly journals Reduced order model of offshore wind turbine wake by proper orthogonal decomposition

2020 ◽  
Vol 82 ◽  
pp. 108554 ◽  
Author(s):  
M. Salman Siddiqui ◽  
Sidra Tul Muntaha Latif ◽  
Muhammad Saeed ◽  
Muhammad Rahman ◽  
Abdul Waheed Badar ◽  
...  
Keyword(s):  
Wind Turbine ◽  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Offshore Wind ◽  
Offshore Wind Turbine ◽  
Order Model ◽  
Reduced Order ◽  
Proper Orthogonal ◽  
Turbine Wake

scholarly journals Construction of reduced-order models for fluid flows using deep feedforward neural networks

2019 ◽  
Vol 872 ◽  
pp. 963-994 ◽  
Author(s):  
Hugo F. S. Lui ◽  
William R. Wolf
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Fluid Flows ◽  
Leading Edge ◽  
Feedforward Neural Networks ◽  
Orthogonal Decomposition ◽  
Reduced Order Models ◽  
Order Model ◽  
Sparse Regression ◽  
Reduced Order ◽  
Proper Orthogonal

We present a numerical methodology for construction of reduced-order models (ROMs) of fluid flows through the combination of flow modal decomposition and regression analysis. Spectral proper orthogonal decomposition is applied to reduce the dimensionality of the model and, at the same time, filter the proper orthogonal decomposition temporal modes. The regression step is performed by a deep feedforward neural network (DNN), and the current framework is implemented in a context similar to the sparse identification of nonlinear dynamics algorithm. A discussion on the optimization of the DNN hyperparameters is provided for obtaining the best ROMs and an assessment of these models is presented for a canonical nonlinear oscillator and the compressible flow past a cylinder. Then the method is tested on the reconstruction of a turbulent flow computed by a large eddy simulation of a plunging airfoil under dynamic stall. The reduced-order model is able to capture the dynamics of the leading edge stall vortex and the subsequent trailing edge vortex. For the cases analysed, the numerical framework allows the prediction of the flow field beyond the training window using larger time increments than those employed by the full-order model. We also demonstrate the robustness of the current ROMs constructed via DNNs through a comparison with sparse regression. The DNN approach is able to learn transient features of the flow and presents more accurate and stable long-term predictions compared to sparse regression.

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