scholarly journals In-Situ Residual Tracking in Reduced Order Modelling

2002 ◽  
Vol 9 (3) ◽  
pp. 105-121 ◽  
Author(s):  
Joseph C. Slater ◽  
Chris L. Pettit ◽  
Philip S. Beran
Keyword(s):  
Evaluation Method ◽  
Operating Conditions ◽  
Further Training ◽  
Order Model ◽  
Reduced Order ◽  
Weighted Residuals ◽  
Reduced Order Modelling ◽  
Estimate Error ◽  
Proper Orthogonal

Proper orthogonal decomposition (POD) based reduced-order modelling is demonstrated to be a weighted residual technique similar to Galerkin's method. Estimates of weighted residuals of neglected modes are used to determine relative importance of neglected modes to the model. The cumulative effects of neglected modes can be used to estimate error in the reduced order model. Thus, once the snapshots have been obtained under prescribed training conditions, the need to perform full-order simulations for comparison is eliminates. This has the potential to allow the analyst to initiate further training when the reduced modes are no longer sufficient to accurately represent the predominant phenomenon of interest. The response of a fluid moving at Mach 1.2 above a panel to a forced localized oscillation of the panel at and away from the training operating conditions is used to demonstrate the evaluation method.

Air Entrainment During Steady-State Web Winding

1997 ◽  
Vol 64 (4) ◽  
pp. 916-922 ◽  
Author(s):  
M. B. Keshavan ◽  
J. A. Wickert
Keyword(s):  
Steady State ◽  
Air Entrainment ◽  
Operating Conditions ◽  
Order Model ◽  
Reduced Order ◽  
Pressure Profiles ◽  
Air Layers ◽  
Entrained Air ◽  
Air Film

As a web is wound at speed onto a roll, a thin layer of air becomes entrapped between it and the incoming web stream. The resulting spiral-shaped air bearing separates adjacent web layers and can extend many wraps into the roll. The air entrained during the winding process increases the propensity for lateral interlayer slippage and damage to the edges of the web. In the present paper, an in situ technique is developed for measuring the thickness of the entrained air film during winding, and parameter studies quantify the effects of such winding variables as tension, width, transport speed, and surface roughness. With a view towards evaluating different transport designs and operating conditions, three measures of air entrainment are discussed: (i) the cumulative thickness of all air layers, (ii) the thickness of the outermost air layer at the nip, and (iii) the rate at which air bleeds from the roll once it comes to rest. Measured values of the first two metrics are compared with those predicted by a derived two-dimensional reduced-order model for steady-state winding. The analysis treats the two bounding configurations of symmetric and asymmetric stacking of web layers by specifying appropriate cross-web pressure profiles.

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 Reduced Order Model of Position Control System

2011 ◽  
pp. 113-115
Author(s):  
Yogesh V. Hote ◽  
A. N. Jha ◽  
J. R. P. Gupta
Keyword(s):  
Control System ◽  
Position Control ◽  
Open Loop ◽  
Simple Approach ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Reduced Order Modelling ◽  
Position Control System

In this paper, simple approach is proposed to determine reduced order model of a unstable open-loop position control system. This approach is based on Krishnamurthy’s approach on Routh criterion on reduced order modelling. The results are simulated in Matlab environment.

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.

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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