scholarly journals Multi-fidelity non-intrusive reduced-order modelling based on manifold alignment

2021 ◽  
Vol 477 (2253) ◽  
pp. 20210495
Author(s):  
Christian Perron ◽  
Dushhyanth Rajaram ◽  
Dimitri N. Mavris
Keyword(s):  
Predictive Accuracy ◽  
Computational Cost ◽  
Predictive Performance ◽  
Reduced Order Model ◽  
Training Data ◽  
Order Model ◽  
Reduced Order ◽  
Reduced Order Modelling ◽  
Manifold Alignment ◽  
Computational Budget

This work presents the development of a multi-fidelity, parametric and non-intrusive reduced-order modelling method to tackle the problem of achieving an acceptable predictive accuracy under a limited computational budget, i.e. with expensive simulations and sparse training data. Traditional multi-fidelity surrogate models that predict scalar quantities address this issue by leveraging auxiliary data generated by a computationally cheaper lower fidelity code. However, for the prediction of field quantities, simulations of different fidelities may produce responses with inconsistent representations, rendering the direct application of common multi-fidelity techniques challenging. The proposed approach uses manifold alignment to fuse inconsistent fields from high- and low-fidelity simulations by individually projecting their solution onto a common latent space. Hence, simulations using incompatible grids or geometries can be combined into a single multi-fidelity reduced-order model without additional manipulation of the data. This method is applied to a variety of multi-fidelity scenarios using a transonic airfoil problem. In most cases, the new multi-fidelity reduced-order model achieves comparable predictive accuracy at a lower computational cost. Furthermore, it is demonstrated that the proposed method can combine disparate fields without any adverse effect on predictive performance.

scholarly journals Reduced-Order Modelling with Domain Decomposition Applied to Multi-Group Neutron Transport

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1369
Author(s):  
Toby R. F. Phillips ◽  
Claire E. Heaney ◽  
Brendan S. Tollit ◽  
Paul N. Smith ◽  
Christopher C. Pain
Keyword(s):  
Domain Decomposition ◽  
Neutron Transport ◽  
Computational Cost ◽  
Basis Functions ◽  
Reduced Order Model ◽  
Test Case ◽  
Order Model ◽  
Reduced Order ◽  
Reduced Order Modelling ◽  
Neutron Transport Equations

Solving the neutron transport equations is a demanding computational challenge. This paper combines reduced-order modelling with domain decomposition to develop an approach that can tackle such problems. The idea is to decompose the domain of a reactor, form basis functions locally in each sub-domain and construct a reduced-order model from this. Several different ways of constructing the basis functions for local sub-domains are proposed, and a comparison is given with a reduced-order model that is formed globally. A relatively simple one-dimensional slab reactor provides a test case with which to investigate the capabilities of the proposed methods. The results show that domain decomposition reduced-order model methods perform comparably with the global reduced-order model when the total number of reduced variables in the system is the same with the potential for the offline computational cost to be significantly less expensive.

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 A Comprehensive CFD Model for Dual-Phase Brass Indirect Extrusion Based on Constitutive Laws: Assessment of Hot-Zone Formation and Failure Prognosis

Metals ◽  
2018 ◽  
Vol 8 (12) ◽  
pp. 1043 ◽  
Author(s):  
George Pashos ◽  
George Pantazopoulos ◽  
Ioannis Contopoulos
Keyword(s):  
Stokes Equations ◽  
Metal Flow ◽  
Computational Cost ◽  
Constitutive Laws ◽  
Reduced Order Model ◽  
Preliminary Evaluation ◽  
Order Model ◽  
Zone Formation ◽  
Reduced Order ◽  
Prediction And Prevention

A numerical method for the precise calculation of temperature, velocity and pressure profiles of the α-β brass indirect hot extrusion process is presented. The method solves the Navier–Stokes equations for non-Newtonian liquids with strain-rate and temperature-dependent viscosity that is formulated using established constitutive laws based on the Zener–Hollomon type equation for plastic flow stress. The method can be implemented with standard computational fluid dynamics (CFD) software, has relatively low computational cost, and avoids the numerical artifacts associated with other methods commonly used for such processes. A response surface technique is also implemented, and it is thus possible to build a reduced order model that approximately maps the process with respect to all combinations of its parameters, including the extrusion speed and brass phase constitution. The reduced order model can be a very useful tool for production, because it instantaneously provides important quantities, such as the average pressure or the temperature of hot-spots that are formed due to the combined effect of die/billet friction and the generation of heat from plastic deformation (adiabatic shear deformation heating). This approach can assist in the preliminary evaluation of the metal flow pattern, and in the prediction and prevention of critical extrusion failures, thus leading to subsequent process and product quality improvements.

Computationally Efficient Approaches to Simulate the Dynamics of Microbeams Under Mechanical Shock

2006 ◽  
Author(s):  
Mohammad I. Younis ◽  
Danial Jordy ◽  
James M. Pitarresi
Keyword(s):  
Hybrid Approach ◽  
Computational Cost ◽  
Nonlinear Behavior ◽  
Reduced Order Model ◽  
Beam Model ◽  
Mechanical Shock ◽  
Computationally Efficient ◽  
Order Model ◽  
Reduced Order ◽  
Dynamic Loading Conditions

We present computationally efficient models and approaches and utilize them to investigate the dynamics of microbeams under mechanical shock. We explore using a hybrid approach utilizing a beam model combined with the shock spectrum of a spring-mass-damper model. We conclude that this approach is computationally efficient and yields accurate results in both quasi-static and dynamic loading conditions. We utilize a reduced-order model based on the nonlinear Euler-Bernoulli beam model. We demonstrate that this model is capable of capturing accurately the dynamic behavior of microbeams under shock pulses of various amplitudes (low-g and high-g), in various damping conditions, structural boundaries (clamped-clamped and clamped-free), and can capture both linear and nonlinear behavior. We investigate high-g loading cases. We report significant increase in the computational cost of simulations when using traditional nonlinear finite-element models because of the activation of higher-order modes. We demonstrate that the developed reduced-order model can be very efficient in such cases.

scholarly journals Development of a Reduced Order Model for Fuel Burnup Analysis

Energies ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 890 ◽  
Author(s):  
Christian Castagna ◽  
Manuele Aufiero ◽  
Stefano Lorenzi ◽  
Guglielmo Lomonaco ◽  
Antonio Cammi
Keyword(s):  
Methodological Approach ◽  
Computational Cost ◽  
Reaction Rates ◽  
Reduced Order Model ◽  
Fuel Burnup ◽  
Order Model ◽  
Reduced Order ◽  
Solution Accuracy ◽  
Proper Orthogonal ◽  
Over Time

Fuel burnup analysis requires a high computational cost for full core calculations, due to the amount of the information processed for the total reaction rates in many burnup regions. Indeed, they reach the order of millions or more by a subdivision into radial and axial regions in a pin-by-pin description. In addition, if multi-physics approaches are adopted to consider the effects of temperature and density fields on fuel consumption, the computational load grows further. In this way, the need to find a compromise between computational cost and solution accuracy is a crucial issue in burnup analysis. To overcome this problem, the present work aims to develop a methodological approach to implement a Reduced Order Model (ROM), based on Proper Orthogonal Decomposition (POD), in fuel burnup analysis. We verify the approach on 4 years of burnup of the TMI-1 unit cell benchmark, by reconstructing fuel materials and burnup matrices over time with different levels of approximation. The results show that the modeling approach is able to reproduce reactivity and nuclide densities over time, where the accuracy increases with the number of basis functions employed.

A Reduced-Order Model for Turbomachinery Flows Using Proper Orthogonal Decomposition

2013 ◽  
Author(s):  
Thomas A. Brenner ◽  
Forrest L. Carpenter ◽  
Brian A. Freno ◽  
Paul G. A. Cizmas
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Stokes Equations ◽  
Computational Cost ◽  
Wheel Speed ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Computational Time ◽  
Order Model ◽  
Reduced Order ◽  
Proper Orthogonal

This paper presents the development of a reduced-order model based on the proper orthogonal decomposition (POD) method. The POD method has been developed to predict turbomachinery flows modeled by the Reynolds-averaged Navier–Stokes equations. The purpose of using a POD-based reduced-order model is to decrease the computational cost of turbomachinery flows. The POD model has been tested for two configurations: a canonical channel with a bump case and the transonic NASA Rotor 67 case. The Rotor 67 case has been simulated at design wheel speed and at three off-design conditions: 70, 80, and 90% of the wheel speed. The results of the POD-based reduced-order model where in excellent agreement with the full-order model results. The computational time of the reduced-order model was approximately one order of magnitude smaller than that of the full-order model.

A Nonlinear Reduced-Order Model for Electrostatic MEMS

2003 ◽  
Author(s):  
Eihab M. Abdel-Rahman ◽  
Mohammad I. Younis ◽  
Ali H. Nayfeh
Keyword(s):  
Equations Of Motion ◽  
Computational Cost ◽  
Design Tool ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Design Parameters ◽  
Mems Devices ◽  
Order Model ◽  
Reduced Order ◽  
Galerkin Procedure

We present an analytical approach and a reduced-order model (macromodel) to investigate the behavior of electrically actuated microbeam-based MEMS. The macromodel provides an effective and accurate design tool for this class of MEMS devices. The macromodel is obtained by discretizing the distributed-parameter system using a Galerkin procedure into a finite-degree-of-freedom system consisting of ordinary-differential equations in time. The macromodel accounts for moderately large deflections, dynamic loads, and the coupling between the mechanical and electrical forces. It accounts for linear and nonlinear elastic restoring forces and the nonlinear electric forces generated by the capacitors. A new technique is developed to represent the electric force in the equations of motion. The new approach allows the use of few linear-undamped mode shapes of a microbeam in its straight position as basis functions in a Galerkin procedure. The macromodel is validated by comparing its results with experimental results and finiteelement solutions available in the literature. Our approach shows attractive features compared to finite-element softwares used in the literature. It is robust over the whole device operation range up to the instability limit of the device (i.e., pull-in). Moreover, it has low computational cost and allows for an easier understanding of the influence of the various design parameters. As a result, it can be of significant benefit to the development of MEMS design software.

A Study of Whole Joint Model Calibration Using Quasi-Static Modal Analysis

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
David A. Najera-Flores ◽  
Robert J. Kuether
Keyword(s):  
Modal Analysis ◽  
Model Calibration ◽  
Computational Cost ◽  
Element Model ◽  
Calibration Method ◽  
Joint Model ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Joint Parameters

Abstract Small length and time scales resulting from high-fidelity frictional contact elements make long duration, low frequency simulations intractable. Alternative reduced order modeling approaches for structural dynamics models have been developed over the last several decades to approximate joint physics based on empirical or mathematical models within a whole joint model representation. The challenge with nonlinear constitutive elements based on empirical models is that the parameters must be calibrated to either experimental or simulation data. This research proposes a model calibration technique that identifies the joint parameters of a four-parameter Iwan element based on the nonlinear natural frequencies and damping ratios computed with quasi-static modal analysis (QSMA). The QSMA algorithm is applied to the full-order finite element model (FEM) to obtain reference data, and a genetic algorithm optimizes the joint parameters within a reduced order model (ROM) by minimizing the difference between the nonlinear modal characteristics for the modes of interest. The calibration method is demonstrated on a C-Beam bolted assembly and the resulting reduced order model is validated by comparing simulations of broadband, forced transient response. The resulting calibrated model captures the nonlinear, multimodal response at a significantly reduced computational cost and can be utilized for producing efficient models that do not have supporting experimental data for calibration.

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