scholarly journals Adaptive reduced-basis generation for reduced-order modeling for the solution of stochastic nondestructive evaluation problems

2016 ◽  
Vol 310 ◽  
pp. 172-188
Author(s):  
Bahram Notghi ◽  
Mohammad Ahmadpoor ◽  
John C. Brigham
Keyword(s):  
Nondestructive Evaluation ◽  
Reduced Order Modeling ◽  
Reduced Basis ◽  
Reduced Order

scholarly journals A Component-Based Parametric Reduced-Order Modeling Method Combined with Substructural Matrix Interpolation and Automatic Sampling

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Ying Liu ◽  
Hongguang Li ◽  
Yun Li ◽  
Huanyu Du
Keyword(s):  
Parameter Space ◽  
Optimal Parameter ◽  
Synthesis Method ◽  
Sampling Procedure ◽  
Reduced Order Modeling ◽  
Modeling Method ◽  
Reduced Basis ◽  
Reduced Order ◽  
Automatic Sampling ◽  
Matrix Interpolation

An efficient parametric reduced-order modeling method combined with substructural matrix interpolation and automatic sampling procedure is proposed. This approach is based on the fixed-interface Craig-Bampton component mode synthesis method (CMS). The novel parametric reduced-order models (PROMs) are developed by interpolating substructural reduced-order matrices. To guarantee the compatibility of the coordinates, we develop a three-step adjustment procedure by reducing the local interface degrees of freedom (DOFs) and performing congruence transformation for the normal modes and interface reduced basis, respectively. In addition, an automatic sampling process is also introduced to dynamically fulfill the predefined error limits. It proceeds by first exploring the parameter space and identifying the sampling points with maximum error indicators for all the parameter-dependent substructures. The exact error of the assembled model at the optimal parameter point is subsequently calculated to determine whether the automatic sampling procedure reaches a desired error tolerance. The proposed framework is then applied to the moving coil of electrical-dynamic shaker to illustrate the advantage and validity. The results indicate that this new approach can significantly reduce both the offline database construction time and online calculation time. Besides, the automatic procedure can sample the parameter space efficiently and fulfill the stopping criterion dynamically with assurance of the resulting PROM accuracy.

scholarly journals Time Stable Reduced Order Modeling by an Enhanced Reduced Order Basis of the Turbulent and Incompressible 3D Navier–Stokes Equations

2019 ◽  
Vol 24 (2) ◽  
pp. 45 ◽  
Author(s):  
Nissrine Akkari ◽  
Fabien Casenave ◽  
Vincent Moureau
Keyword(s):  
Stokes Equations ◽  
A Priori ◽  
Order Reduction ◽  
Reduced Order Modeling ◽  
Reduced Order Model ◽  
Navier Stokes ◽  
Reduced Basis ◽  
Order Model ◽  
Navier Stokes Equations ◽  
Reduced Order

In the following paper, we consider the problem of constructing a time stable reduced order model of the 3D turbulent and incompressible Navier–Stokes equations. The lack of stability associated with the order reduction methods of the Navier–Stokes equations is a well-known problem and, in general, it is very difficult to account for different scales of a turbulent flow in the same reduced space. To remedy this problem, we propose a new stabilization technique based on an a priori enrichment of the classical proper orthogonal decomposition (POD) modes with dissipative modes associated with the gradient of the velocity fields. The main idea is to be able to do an a priori analysis of different modes in order to arrange a POD basis in a different way, which is defined by the enforcement of the energetic dissipative modes within the first orders of the reduced order basis. This enables us to model the production and the dissipation of the turbulent kinetic energy (TKE) in a separate fashion within the high ranked new velocity modes, hence to ensure good stability of the reduced order model. We show the importance of this a priori enrichment of the reduced basis, on a typical aeronautical injector with Reynolds number of 45,000. We demonstrate the capacity of this order reduction technique to recover large scale features for very long integration times (25 ms in our case). Moreover, the reduced order modeling (ROM) exhibits periodic fluctuations with a period of 2 . 2 ms corresponding to the time scale of the precessing vortex core (PVC) associated with this test case. We will end this paper by giving some prospects on the use of this stable reduced model in order to perform time extrapolation, that could be a strategy to study the limit cycle of the PVC.

How Adaptively Constructed Reduced Order Models Can Benefit Sampling-Based Methodsfor Reliability Analyses

2016 ◽  
Vol 23 (05) ◽  
pp. 1650019 ◽  
Author(s):  
Christian Gogu ◽  
Anirban Chaudhuri ◽  
Christian Bes
Keyword(s):  
Finite Element ◽  
Monte Carlo ◽  
Reliability Analysis ◽  
Computational Cost ◽  
Reduced Order Modeling ◽  
Finite Element Models ◽  
Reduced Order Models ◽  
Reduced Basis ◽  
Reduced Order ◽  
Separable Monte Carlo

Many sampling-based approaches are currently available for calculating the reliability of a design. The most efficient methods can achieve reductions in the computational cost by one to several orders of magnitude compared to the basic Monte Carlo method. This paper is specifically targeted at sampling-based approaches for reliability analysis, in which the samples represent calls to expensive finite element models. The aim of this paper is to illustrate how these methods can further benefit from reduced order modeling to achieve drastic additional computational cost reductions, in cases where the reliability analysis is carried out on finite element models. Standard Monte Carlo, importance sampling, separable Monte Carlo and a combined importance separable Monte Carlo approach are presented and coupled with reduced order modeling. An adaptive construction of the reduced basis models is proposed. The various approaches are compared on a thermal reliability design problem, where the coupling with the adaptively constructed reduced order models is shown to further increase the computational efficiency by up to a factor of six.

scholarly journals A Comprehensive Deep Learning-Based Approach to Reduced Order Modeling of Nonlinear Time-Dependent Parametrized PDEs

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Stefania Fresca ◽  
Luca Dede’ ◽  
Andrea Manzoni
Keyword(s):  
Deep Learning ◽  
Reduced Order Modeling ◽  
Time Dependent ◽  
Reduced Basis ◽  
Reduced Order ◽  
Nonlinear Approach ◽  
Parameter Values ◽  
Proper Orthogonal ◽  
Convection Dominated ◽  
Very High

AbstractConventional reduced order modeling techniques such as the reduced basis (RB) method (relying, e.g., on proper orthogonal decomposition (POD)) may incur in severe limitations when dealing with nonlinear time-dependent parametrized PDEs, as these are strongly anchored to the assumption of modal linear superimposition they are based on. For problems featuring coherent structures that propagate over time such as transport, wave, or convection-dominated phenomena, the RB method may yield inefficient reduced order models (ROMs) when very high levels of accuracy are required. To overcome this limitation, in this work, we propose a new nonlinear approach to set ROMs by exploiting deep learning (DL) algorithms. In the resulting nonlinear ROM, which we refer to as DL-ROM, both the nonlinear trial manifold (corresponding to the set of basis functions in a linear ROM) as well as the nonlinear reduced dynamics (corresponding to the projection stage in a linear ROM) are learned in a non-intrusive way by relying on DL algorithms; the latter are trained on a set of full order model (FOM) solutions obtained for different parameter values. We show how to construct a DL-ROM for both linear and nonlinear time-dependent parametrized PDEs. Moreover, we assess its accuracy and efficiency on different parametrized PDE problems. Numerical results indicate that DL-ROMs whose dimension is equal to the intrinsic dimensionality of the PDE solutions manifold are able to efficiently approximate the solution of parametrized PDEs, especially in cases for which a huge number of POD modes would have been necessary to achieve the same degree of accuracy.

scholarly journals REDUCED-ORDER MODELLING OF PARAMETERIZED TRANSIENT FLOWS IN CLOSED-LOOP SYSTEMS

2021 ◽  
Vol 247 ◽  
pp. 06055
Author(s):  
Péter German ◽  
Mauricio Tano ◽  
Jean C. Ragusa ◽  
Carlo Fiorina
Keyword(s):  
Stokes Equations ◽  
Momentum Equation ◽  
Equation Model ◽  
Reduced Order Modeling ◽  
Galerkin Projection ◽  
Reduced Basis ◽  
Reduced Order ◽  
Transient Flows ◽  
Continuity Equations ◽  
The One

In this paper, two Galerkin projection based reduced basis approaches are investigated for the reduced-order modeling of parameterized incompressible Navier-Stokes equations for laminar transient flows. The first approach solves only the reduced momentum equation with additional, physics-based approximations for the dynamics of the pressure field. On the other hand, the second approach solves both the reduced momentum and continuity equations. The reduced bases for the velocity and pressure fields are generated using the method of snapshots combined with Proper Orthogonal Decomposition (POD) for data compression. To remedy the stability issues of the two-equation model, the reduced basis of the velocity is enriched with supremizer functions. Both reduced-order modeling approaches have been implemented in GeN-Foam, an OpenFOAM-based multi-physics solver. A numerical example is presented using a two-dimensional axisymmetric model of the Molten Salt Fast Reactor (MSFR) and the dynamic viscosity as the uncertain parameter. The results indicate that the one-equation model is slightly more accurate in terms of velocity, while the two-equation model, built with the same amount of modes for the velocity, is far more accurate in terms of pressure. The speed-up factors for the reduced-order models are 3060 for the one-equation model and 2410 for the two-equation model.

Lattice Boltzmann Flow Simulations With Applications of Reduced Order Modeling Techniques.

2014 ◽  
Author(s):  
Donald L. Brown ◽  
Jun Li ◽  
Victor M. Calo ◽  
Mehdi Ghommem ◽  
Yalchin Efendiev
Keyword(s):  
Lattice Boltzmann ◽  
Reduced Order Modeling ◽  
Reduced Order ◽  
Flow Simulations ◽  
Modeling Techniques
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