Thermal Response Variability of Random Polycrystalline Microstructures

AbstractA data-driven model reduction strategy is presented for the representation of random polycrystal microstructures. Given a set of microstructure snapshots that satisfy certain statistical constraints such as given low-order moments of the grain size distribution, using a non-linear manifold learning approach, we identify the intrinsic low-dimensionality of the microstructure manifold. In addition to grain size, a linear dimensionality reduction technique (Karhunun-Loéve Expansion) is used to reduce the texture representation. The space of viable microstructures is mapped to a low-dimensional region thus facilitating the analysis and design of polycrystal microstructures. This methodology allows us to sample microstructure features in the reduced-order space thus making it a highly efficient, low-dimensional surrogate for representing microstructures (grain size and texture). We demonstrate the model reduction approach by computing the variability of homogenized thermal properties using sparse grid collocation in the reduced-order space that describes the grain size and orientation variability.

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Transonic Axial Compressors Loss Correlations: Part I — Analysis and Update of Loss Models

Volume 2A: Turbomachinery ◽

10.1115/gt2020-14713 ◽

2020 ◽

Author(s):

Marco Manfredi ◽

Fabrizio Fontaneto

Keyword(s):

Axial Compressor ◽

Reduced Order ◽

Axial Compressors ◽

Analysis And Design ◽

Main Driver ◽

Validity Range ◽

Loss Models ◽

Generation Mechanisms ◽

Semi Empirical ◽

System Designs

Abstract The quest for greener, more efficient aircraft engines is the main driver for the development of innovative compression system designs. Reduced order design tools rely nevertheless on semi-empirical loss models, whose validity range is often not net or in general not verified. The present work aims at defining a set of loss correlations, which could readily be employed in the analysis and design process of modern transonic axial compressors. In part I, the main entropy generation mechanisms are described together with a review of the most commonly employed modelling approaches. Selected loss models are then deeper investigated and updated to increase both their range of validity and the accuracy of their predictions. In Part II, the effectiveness of the investigated models will be tested for one specific low aspect ratio axial compressor stage.

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A Physics-Based Dynamic Model for Boilers: Part 2 — Model Reduction in a Cogeneration Application

Volume 6: Ceramics; Controls, Diagnostics and Instrumentation; Education; Manufacturing Materials and Metallurgy ◽

10.1115/gt2017-63546 ◽

2017 ◽

Author(s):

Matthew J. Blom ◽

Michael J. Brear ◽

Chris G. Manzie ◽

Ashley P. Wiese

Keyword(s):

Model Reduction ◽

Gas Turbine ◽

Dynamic Model ◽

Reduction Process ◽

Singular Perturbation Theory ◽

Reduced Order Models ◽

Reduced Order ◽

One Dimensional ◽

Time Scale Separation ◽

Modelling Framework

This paper is the second part of a two part study that develops, validates and integrates a one-dimensional, physics-based, dynamic boiler model. Part 1 of this study [1] extended and validated a particular modelling framework to boilers. This paper uses this framework to first present a higher order model of a gas turbine based cogeneration plant. The significant dynamics of the cogeneration system are then identified, corresponding to states in the gas path, the steam path, the gas turbine shaft, gas turbine wall temperatures and boiler wall temperatures. A model reduction process based on time scale separation and singular perturbation theory is then demonstrated. Three candidate reduced order models are identified using this model reduction process, and the simplest, acceptable dynamic model of this integrated plant is found to require retention of both the gas turbine and boiler wall temperature dynamics. Subsequent analysis of computation times for the original physics-based one-dimensional model and the candidate, reduced order models demonstrates that significantly faster than real time simulation is possible in all cases. Furthermore, with systematic replacement of the algebraic states with feedforward maps in the reduced order models, further computational savings of up to one order of magnitude can be achieved. This combination of model fidelity and computational tractability suggest suggests that the resulting reduced order models may be suitable for use in model based control of cogeneration plants.

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Phosphate tungsten bronze series: crystallographic and structural properties of low-dimensional conductors

Acta Crystallographica Section B Structural Science ◽

10.1107/s0108768101009685 ◽

2001 ◽

Vol 57 (5) ◽

pp. 603-632 ◽

Cited By ~ 32

Author(s):

P. Roussel ◽

O. Pérez ◽

Ph. Labbé

Keyword(s):

Crystal Structures ◽

Structural Properties ◽

Tungsten Bronze ◽

Structural Description ◽

X Ray ◽

X Ray Scattering ◽

Modulated Structures ◽

Low Dimensionality ◽

Low Dimensional ◽

Thickness Function

Phosphate tungsten bronzes have been shown to be conductors of low dimensionality. A review of the crystallographic and structural properties of this huge series of compounds is given here, corresponding to the present knowledge of the different X-ray studies and electron microscopy investigations. Three main families are described, monophosphate tungsten bronzes, Ax (PO2)4(WO3)2m , either with pentagonal tunnels (MPTBp) or with hexagonal tunnels (MPTBh), and diphosphate tungsten bronzes, Ax (P2O4)2(WO3)2m , mainly with hexagonal tunnels (DPTBh). The general aspect of these crystal structures may be described as a building of polyhedra sharing oxygen corners made of regular stacking of WO3-type slabs with a thickness function of m, joined by slices of tetrahedral PO4 phosphate or P2O7 diphosphate groups. The relations of the different slabs with respect to the basic perovskite structure are mentioned. The structural description is focused on the tilt phenomenon of the WO6 octahedra inside a slab of WO3-type. In this respect, a comparison with the different phases of the WO3 crystal structures is established. The various modes of tilting and the different possible connections between two adjacent WO3-type slabs involve a great variety of structures with different symmetries, as well as the existence of numerous twins in MPTBp's. Several phase transitions, with the appearance of diffuse scattering and modulation phenomena, were analysed by X-ray scattering measurements and through the temperature dependence of various physical properties for the MPTBp's. The role of the W displacements within the WO3-type slabs, in two modulated structures (m = 4 and m = 10), already solved, is discussed. Finally, the complexity of the structural aspects of DPTBh's is explained on the basis of the average structures which are the only ones solved.

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

Journal of Fluid Mechanics ◽

10.1017/s0022112009006363 ◽

2009 ◽

Vol 629 ◽

pp. 41-72 ◽

Cited By ~ 66

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.

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Non-intrusive nonlinear model reduction via machine learning approximations to low-dimensional operators

Advanced Modeling and Simulation in Engineering Sciences ◽

10.1186/s40323-021-00213-5 ◽

2021 ◽

Vol 8 (1) ◽

Author(s):

Zhe Bai ◽

Liqian Peng

Keyword(s):

Machine Learning ◽

Nonlinear Dynamical Systems ◽

Reduced Order Models ◽

Simulation Code ◽

Nonlinear Dynamical ◽

Reduced Order ◽

Nonlinear Model Reduction ◽

Regression Techniques ◽

Low Dimensional ◽

Modern Machine

AbstractAlthough projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing such a reduced-order model typically requires significant modifications to the underlying simulation code. To address this, we propose a method that enables traditionally intrusive reduced-order models to be accurately approximated in a non-intrusive manner. Specifically, the approach approximates the low-dimensional operators associated with projection-based reduced-order models (ROMs) using modern machine-learning regression techniques. The only requirement of the simulation code is the ability to export the velocity given the state and parameters; this functionality is used to train the approximated low-dimensional operators. In addition to enabling nonintrusivity, we demonstrate that the approach also leads to very low computational complexity, achieving up to $$10^3{\times }$$ 10 3 × in run time. We demonstrate the effectiveness of the proposed technique on two types of PDEs. The domain of applications include both parabolic and hyperbolic PDEs, regardless of the dimension of full-order models (FOMs).

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Parameter tuning of reduced order evaporator models via numerical model reduction

2008 American Control Conference ◽

10.1109/acc.2008.4586696 ◽

2008 ◽

Cited By ~ 1

Author(s):

Abhishek Gupta ◽

Bryan P. Rasmussen

Keyword(s):

Numerical Model ◽

Model Reduction ◽

Parameter Tuning ◽

Reduced Order

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Toward Optimality of Proper Generalised Decomposition Bases

Mathematical and Computational Applications ◽

10.3390/mca24010030 ◽

2019 ◽

Vol 24 (1) ◽

pp. 30 ◽

Cited By ~ 1

Author(s):

Shadi Alameddin ◽

Amélie Fau ◽

David Néron ◽

Pierre Ladevèze ◽

Udo Nackenhorst

Keyword(s):

Greedy Algorithms ◽

Order Reduction ◽

Nonlinear Material ◽

Proper Generalized Decomposition ◽

Model Order ◽

Reduced Order ◽

Structural Problems ◽

Low Dimensional ◽

Value Decomposition ◽

The Greedy Algorithm

The solution of structural problems with nonlinear material behaviour in a model order reduction framework is investigated in this paper. In such a framework, greedy algorithms or adaptive strategies are interesting as they adjust the reduced order basis (ROB) to the problem of interest. However, these greedy strategies may lead to an excessive increase in the size of the ROB, i.e., the solution is no more represented in its optimal low-dimensional expansion. Here, an optimised strategy is proposed to maintain, at each step of the greedy algorithm, the lowest dimension of a Proper Generalized Decomposition (PGD) basis using a randomised Singular Value Decomposition (SVD) algorithm. Comparing to conventional approaches such as Gram–Schmidt orthonormalisation or deterministic SVD, it is shown to be very efficient both in terms of numerical cost and optimality of the ROB. Examples with different mesh densities are investigated to demonstrate the numerical efficiency of the presented method.

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Study of Fault Diagnosis Based on Manifold Learning

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.312.650 ◽

2013 ◽

Vol 312 ◽

pp. 650-654 ◽

Cited By ~ 1

Author(s):

Yi Lin He ◽

Guang Bin Wang ◽

Fu Ze Xu

Keyword(s):

Fault Diagnosis ◽

Manifold Learning ◽

Linear Manifold ◽

Rotating Machinery ◽

Dimensional Manifold ◽

Advantages And Disadvantages ◽

Non Linear ◽

Future Direction ◽

Low Dimensional ◽

Machinery Fault Diagnosis

Characteristic signals in rotating machinery fault diagnosis with the issues of complex and difficult to deal with, while the use of non-linear manifold learning method can effectively extract low-dimensional manifold characteristics embedded in the high-dimensional non-linear data. It greatly maintains the overall geometric structure of the signals and improves the efficiency and reliability of the rotating machinery fault diagnosis. According to the development prospects of manifold learning, this paper describes four classical manifold learning methods and each advantages and disadvantages. It reviews the research status and application of fault diagnosis based on manifold learning, as well as future direction of researches in the field of manifold learning fault diagnosis.

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An Energy Closure Criterion for Model Reduction of a Kicked Euler–Bernoulli Beam

Journal of Vibration and Acoustics ◽

10.1115/1.4048663 ◽

2020 ◽

Vol 143 (4) ◽

Author(s):

Suparno Bhattacharyya ◽

Joseph P. Cusumano

Keyword(s):

Model Reduction ◽

Mode Selection ◽

Computational Cost ◽

Impulsive Loading ◽

Bernoulli Beam ◽

Full System ◽

Fixed Amount ◽

Reduced Order ◽

Proper Orthogonal ◽

Euler Bernoulli Beam

Abstract Reduced order models (ROMs) can be simulated with lower computational cost while being more amenable to theoretical analysis. Here, we examine the performance of the proper orthogonal decomposition (POD), a data-driven model reduction technique. We show that the accuracy of ROMs obtained using POD depends on the type of data used and, more crucially, on the criterion used to select the number of proper orthogonal modes (POMs) used for the model. Simulations of a simply supported Euler–Bernoulli beam subjected to periodic impulsive loads are used to generate ROMs via POD, which are then simulated for comparison with the full system. We assess the accuracy of ROMs obtained using steady-state displacement, velocity, and strain fields, tuning the spatiotemporal localization of applied impulses to control the number of excited modes in, and hence the dimensionality of, the system’s response. We show that conventional variance-based mode selection leads to inaccurate models for sufficiently impulsive loading and that this poor performance is explained by the energy imbalance on the reduced subspace. Specifically, the subspace of POMs capturing a fixed amount (say, 99.9%) of the total variance underestimates the energy input and dissipated in the ROM, yielding inaccurate reduced-order simulations. This problem becomes more acute as the loading becomes more spatio-temporally localized (more impulsive). Thus, energy closure analysis provides an improved method for generating ROMs with energetics that properly reflect that of the full system, resulting in simulations that accurately represent the system’s true behavior.

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