scholarly journals On error estimation for reduced-order modeling of linear non-parametric and parametric systems

2021 ◽  
Author(s):  
Lihong Feng ◽  
Peter Benner
Keyword(s):  
Reduced Order Modeling ◽  
Reduced Order Model ◽  
Error Estimator ◽  
Linear Dynamical System ◽  
Order Model ◽  
Reduced Order ◽  
Error Estimators ◽  
Theoretical Results ◽  
Parametric Systems ◽  
Better Than

Motivated by a recently proposed error estimator for the transfer function of the reduced-order model of a given linear dynamical system, we further develop more theoretical results in this work. Moreover, we propose several variants of the error estimator, and compare those variants with the existing ones both theoretically and numerically. It is shown that some of the proposed error estimators perform better than or equally well as the existing ones. All the error estimators considered can be easily extended to estimate the output error of reduced-order modeling for steady linear parametric systems.

scholarly journals Evolve Then Filter Regularization for Stochastic Reduced Order Modeling

2018 ◽  
Author(s):  
Xuping Xie ◽  
Feng Bao ◽  
Clayton G. Webster
Keyword(s):  
Stochastic Systems ◽  
Spatial Filter ◽  
Reduced Order Modeling ◽  
Reduced Order Model ◽  
Galerkin Projection ◽  
Order Model ◽  
Reduced Order ◽  
Stochastic Burgers Equation ◽  
Numerical Stabilization ◽  
Convection Dominated

In this paper, we introduce the evolve-then-filter (EF) regularization method for reduced order modeling of convection-dominated stochastic systems. The standard Galerkin projection reduced order model (G-ROM) yield numerical oscillations in a convection-dominated regime. The evolve-then-filter reduced order model (EF-ROM) aims at the numerical stabilization of the standard G-ROM, which uses explicit ROM spatial filter to regularize various terms in the reduced order model (ROM). Our numerical results based on a stochastic Burgers equation with linear multiplicative noise. It shows that the EF-ROM is significantly better results than G-ROM.

Reduced Order Modeling of Entrained Flow Solid Fuel Gasification

2009 ◽  
Author(s):  
Rory F. D. Monaghan ◽  
Mayank Kumar ◽  
Simcha L. Singer ◽  
Cheng Zhang ◽  
Ahmed F. Ghoniem
Keyword(s):  
Fluid Dynamics ◽  
Reduced Order Modeling ◽  
Combined Cycle ◽  
Reduced Order Model ◽  
Temperature Profiles ◽  
Order Model ◽  
External Temperature ◽  
Reduced Order ◽  
Entrained Flow ◽  
Entrained Flow Gasifiers

Reduced order models that accurately predict the operation of entrained flow gasifiers as components within integrated gasification combined cycle (IGCC) or polygeneration plants are essential for greater commercialization of gasification-based energy systems. A reduced order model, implemented in Aspen Custom Modeler, for entrained flow gasifiers that incorporates mixing and recirculation, rigorously calculated char properties, drying and devolatilization, chemical kinetics, simplified fluid dynamics, heat transfer, slag behavior and syngas cooling is presented. The model structure and submodels are described. Results are presented for the steady-state simulation of a two-metric-tonne-per-day (2 tpd) laboratory-scale Mitsubishi Heavy Industries (MHI) gasifier, fed by two different types of coal. Improvements over the state-of-the-art for reduced order modeling include the ability to incorporate realistic flow conditions and hence predict the gasifier internal and external temperature profiles, the ability to easily interface the model with plant-wide flowsheet models, and the flexibility to apply the same model to a variety of entrained flow gasifier designs. Model validation shows satisfactory agreement with measured values and computational fluid dynamics (CFD) results for syngas temperature profiles, syngas composition, carbon conversion, char flow rate, syngas heating value and cold gas efficiency. Analysis of the results shows the accuracy of the reduced order model to be similar to that of more detailed models that incorporate CFD. Next steps include the activation of pollutant chemistry and slag submodels, application of the reduced order model to other gasifier designs, parameter studies and uncertainty analysis of unknown and/or assumed physical and modeling parameters, and activation of dynamic simulation capability.

scholarly journals A Block Arnoldi Algorithm Based Reduced-Order Model Applied to Large-Scale Algebraic Equations of a 3-D Field Problem

2021 ◽  
Vol 11 (20) ◽  
pp. 9435
Author(s):  
Ning Wang ◽  
Jiajia Chen ◽  
Huifang Wang ◽  
Shiyou Yang
Keyword(s):  
Temperature Field ◽  
Reduction Process ◽  
Reduced Order Model ◽  
Error Estimator ◽  
Transient Field ◽  
Order Model ◽  
Field Problem ◽  
Reduced Order ◽  
Arnoldi Algorithm ◽  
Block Arnoldi

In simulations of three-dimensional transient physics filled through a numerical approach, the order of the equation set of high-fidelity models is extremely high. To eliminate the large dimension of equations, a model order reduction (MOR) technique is introduced. In the existing MOR methods, the block Arnoldi algorithm-based MOR method is numerically stable, achieving a passively reduced order model. Nevertheless, this method performs poorly when it is applied to very wide-frequency transients. To eliminate this deficiency, multipoint MOR methods are emerging. However, it is hard to directly apply an existing multipoint MOR method to a 3-D transient field equation set. The implementation issues in a reduction process (such as the selection of expansion points, the number of moments matched at a point and the error bound) have not been explored in detail. In this respect, an adaptive multipoint model reduction model based on the Arnoldi algorithm is proposed to obtain the reduced-order models of a 3-D temperature field. The originality of this study is the proposal of a novel adaptive algorithm for selecting expansion points, matching moments automatically, using a posterior-error estimator based on temperature response coupled with a network topological method (NTM). The computational efficiency and accuracy of the proposed method are evaluated by the numerical results from solving the temperature field of a prototype insulated-gate bipolar transistor (IGBT).

Reduced-Order Modeling of Two-Sided Frictional Interfaces

2007 ◽  
Author(s):  
Jason D. Miller ◽  
D. Dane Quinn
Keyword(s):  
Modal Analysis ◽  
Computational Efficiency ◽  
Order Approximation ◽  
Reduced Order Modeling ◽  
Original Model ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Overall Response

We consider a model describing the behavior of a two-sided interface allowing for both elasticity and microslip of the joint. A reduced-order approximation of this system is developed based on a decomposition of the original model into an elastic chain and a dissipative component equivalent to a series-series Iwan chain. The Iwan chain is then solved using a quasi-static complementarity formulation while the order of the elastic chain is reduced using modal analysis. The computational efficiency of the resulting reduced-order model is significantly increased, while the overall response of the interface to realistic forcing conditions is maintained.

scholarly journals Computer Vision with Error Estimation for Reduced Order Modeling of Macroscopic Mechanical Tests

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Franck Nguyen ◽  
Selim M. Barhli ◽  
Daniel Pino Muñoz ◽  
David Ryckelynck
Keyword(s):  
Neural Network ◽  
Computer Vision ◽  
Convolutional Neural Network ◽  
Digital Image ◽  
Mechanical Test ◽  
Reduced Order Model ◽  
Error Estimator ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order

In this paper, computer vision enables recommending a reduced order model for fast stress prediction according to various possible loading environments. This approach is applied on a macroscopic part by using a digital image of a mechanical test. We propose a hybrid approach that simultaneously exploits a data-driven model and a physics-based model, in mechanics of materials. During a machine learning stage, a classification of possible reduced order models is obtained through a clustering of loading environments by using simulation data. The recognition of the suitable reduced order model is performed via a convolutional neural network (CNN) applied to a digital image of the mechanical test. The CNN recommend a convenient mechanical model available in a dictionary of reduced order models. The output of the convolutional neural network being a model, an error estimator, is proposed to assess the accuracy of this output. This article details simple algorithmic choices that allowed a realistic mechanical modeling via computer vision.

Reduced Order Modeling Based on Complex Nonlinear Modal Analysis and its Application to Bladed Disks With Shroud Contact

2013 ◽  
Author(s):  
Malte Krack ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek ◽  
Christian Siewert ◽  
Andreas Hartung
Keyword(s):  
Modal Analysis ◽  
Limit Cycle ◽  
Large Scale ◽  
Computational Effort ◽  
Reduced Order Modeling ◽  
Forced Response ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Nonlinear Modal Analysis

The design of bladed disks with contact interfaces typically requires analyses of the resonant forced response and flutter-induced limit cycle oscillations. The steady-state vibration behavior can efficiently be calculated using the Multi-Harmonic Balance method. The dimension of the arising algebraic systems of equations is essentially proportional to the number of harmonics and the number of degrees of freedom (DOFs) retained in the model. Extensive parametric studies necessary e.g. for robust design optimization are often not possible in practice due to the resulting computational effort. In this paper, a two-step nonlinear reduced order modeling approach is proposed. First, the autonomous nonlinear system is analyzed using a Complex Nonlinear Modal Analysis technique based on the work of Laxalde and Thouverez [1]. The methodology in [1] was refined by an exact condensation approach as well as analytical calculation of gradients in order to efficiently study localized nonlinearities in large-scale systems. Moreover, a continuation method was employed in order to predict nonlinear modal interactions. Modal properties such as eigenfrequency and modal damping are directly calculated with respect to the kinetic energy in the system. In a second step, a reduced order model is built based on the Single Nonlinear Resonant Mode theory. It is shown that linear damping and harmonic forcing can be superimposed. Moreover, similarity properties can be exploited to vary normal preload or gap values in contact interfaces. Thus, a large parameter space can be covered without the need for re-computation of nonlinear modal properties. The computational effort for evaluating the reduced order model is almost negligible since it contains a single DOF only, independent of the original system. The methodology is applied to both a simplified and a large-scale model of a bladed disk with shroud contact interfaces. In contrast to [1], the contact constraints account for variable normal load and lift-off in addition to dry friction. Forced response functions, backbone curves for varying normal preload and excitation level as well as flutter-induced limit cycle oscillations are analysed and compared to conventional methods. The limits of the proposed methodology are indicated and discussed.

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.

scholarly journals Adaptive POD-DEIM model reduction based on an improved error estimator

2018 ◽  
Author(s):  
Sridhar Chellappa ◽  
Lihong Feng ◽  
Peter Benner
Keyword(s):  
Dynamical Systems ◽  
Model Reduction ◽  
Nonlinear Model ◽  
Reduced Order Model ◽  
Error Estimator ◽  
Order Model ◽  
Reduced Order ◽  
Nonlinear Model Reduction ◽  
Nonlinear Approximations ◽  
Output Error

For reliable, efficient, rapid simulations of dynamical systems, a reduced order model (ROM) with certified accuracy is highly desirable. The ROM is derived from a full order model (FOM) through model reduction. In this work, we propose an adaptive approach for nonlinear model reduction by making use of a suitable output error estimator, thus enable the generation of a compact ROM, with appropriate balance between the state and nonlinear approximations.

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.

Sign in / Sign up

Export Citation Format

Share Document