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

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.

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Airfoil Optimization Method Based on Convolutional Neural Network Aerodynamic Reduced Order Model

应用数学和力学 ◽

10.21656/1000-0887.420137 ◽

2021 ◽

Vol 43 (0) ◽

pp. 1-7

Author(s):

WANG Muchen ◽

◽

LI Lizhou ◽

ZHANG Jun ◽

...

Keyword(s):

Neural Network ◽

Convolutional Neural Network ◽

Optimization Method ◽

Reduced Order Model ◽

Order Model ◽

Reduced Order ◽

Airfoil Optimization

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Data-driven reduced order model with temporal convolutional neural network

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2019.112766 ◽

2020 ◽

Vol 360 ◽

pp. 112766 ◽

Cited By ~ 8

Author(s):

Pin Wu ◽

Junwu Sun ◽

Xuting Chang ◽

Wenjie Zhang ◽

Rossella Arcucci ◽

...

Keyword(s):

Neural Network ◽

Convolutional Neural Network ◽

Reduced Order Model ◽

Data Driven ◽

Order Model ◽

Reduced Order

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Dynamic Analysis of a Protein-Ligand Molecular Chain Attached to an Atomic Force Microscope

Journal of Vibration and Acoustics ◽

10.1115/1.1804999 ◽

2004 ◽

Vol 126 (4) ◽

pp. 496-513 ◽

Cited By ~ 1

Author(s):

Deman Tang ◽

Earl H. Dowell

Keyword(s):

Nonlinear Systems ◽

Atomic Force Microscope ◽

Reduced Order Model ◽

Molecular Chain ◽

Static Equilibrium ◽

Reduced Order Models ◽

Base Excitation ◽

Order Model ◽

Reduced Order ◽

Atomic Force

Dynamic numerical simulation of a protein-ligand molecular chain connected to a moving atomic force microscope (AFM) has been studied. A sinusoidal base excitation of the cantilevered beam of the AFM is considered in some detail. A comparison between results for a single molecule and those for multiple molecules has been made. For a small number of molecules, multiple stable static equilibrium positions are observed and chaotic behavior may be generated via a period-doubling cascade for harmonic base excitation of the AFM. For many molecules in the chain, only a single static equilibrium position exists. To enable these calculations, reduced-order (dynamic) models are constructed for fully linear, combined linear/nonlinear and fully nonlinear systems. Several distinct reduced-order models have been developed that offer the option of increased computational efficiency at the price of greater effort to construct the particular reduced-order model. The agreement between the original and reduced-order models (ROM) is very good even when only one mode is included in the ROM for either the fully linear or combined linear/nonlinear systems provided the excitation frequency is lower than the fundamental natural frequency of the linear system. The computational advantage of the reduced-order model is clear from the results presented.

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Experimental Validation of Neural-Network-Based Nonlinear Reduced-Order Model for Vertical Sloshing

10.2514/6.2022-1186 ◽

2022 ◽

Author(s):

Marco Pizzoli ◽

Francesco Saltari ◽

Giuliano Coppotelli ◽

Franco Mastroddi

Keyword(s):

Neural Network ◽

Experimental Validation ◽

Reduced Order Model ◽

Order Model ◽

Reduced Order

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A Reduced Order Model of Mistuning Using a Subset of Nominal System Modes

Volume 4: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education; IGTI Scholar Award; General ◽

10.1115/99-gt-288 ◽

1999 ◽

Cited By ~ 5

Author(s):

M.-T. Yang ◽

J. H. Griffin

Keyword(s):

Degrees Of Freedom ◽

Reduced Order Model ◽

Reduced Order Models ◽

Order Model ◽

Disk System ◽

Element Analysis ◽

Reduced Order ◽

Nominal System ◽

Harmonic Response ◽

Bladed Disk

Reduced order models have been reported in the literature that can be used to predict the harmonic response of mistuned bladed disks. It has been shown that in many cases they exhibit structural fidelity comparable to a finite element analysis of the full bladed disk system while offering a significant improvement in computational efficiency. In these models the blades and disk are treated as distinct substructures. This paper presents a new, simpler approach for developing reduced order models in which the modes of the mistuned system are represented in terms of a sub-set of nominal system modes. It has the following attributes: the input requirements are relatively easy to generate; it accurately predicts mistuning effects in regions where frequency veering occurs; as the number of degrees of freedom increases it converges to the exact solution; it accurately predicts stresses as well as displacements; and it accurately models the deformation and stresses at the blades’ bases.

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Accuracies of Reduced Order Models of a Bladed Rotor With Geometric Mistuning

Journal of Turbomachinery ◽

10.1115/1.4025666 ◽

2013 ◽

Vol 136 (7) ◽

Cited By ~ 2

Author(s):

Yasharth Bhartiya ◽

Alok Sinha

Keyword(s):

Natural Frequencies ◽

Domain Analysis ◽

Forced Response ◽

Reduced Order Model ◽

Mode Shapes ◽

Reduced Order Models ◽

Order Model ◽

Reduced Order ◽

Model Based ◽

Bladed Rotor

The results from a reduced order model based on frequency mistuning are compared with those from recently developed modified modal domain analysis (MMDA). For the academic bladed rotor considered in this paper, the frequency mistuning analysis is unable to capture the effects of geometric mistuning, whereas MMDA provides accurate estimates of natural frequencies, mode shapes, and forced response.

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Generation of Equivalent Circuit Models From Simulation Data of a Thermal System

Heat Transfer, Volume 7 ◽

10.1115/imece2002-33789 ◽

2002 ◽

Author(s):

M. Bikdash ◽

Y. P. Pang ◽

E. P. Scott

Keyword(s):

Complete Solution ◽

Electrical Circuit ◽

Reduced Order Model ◽

Thermal System ◽

Reduced Order Models ◽

Order Model ◽

Simulation Data ◽

Cooling Fluid ◽

Reduced Order ◽

High Level

To enable the design and analysis of Integrated Power Electronics Models (IPEMs), a high level of software integration is needed. The solvers needed range form electrical circuit simulators, like Saber, to thermal analysis and CFD solvers like I-DEAS. As an electrical design parameter is changed, its effect will, in principle, be felt all the way to the temperature distribution in the cooling fluid, and hence a complete solution of the temperature field may have to be recomputed. This is of course computationally prohibitive. Hence a reduced-order model of the thermal behavior of the heat sink is of great interest. In this paper, we will present an algorithm that can automatically generate these reduced-order models from finite-element simulations.

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Order Reduction of Parametrically Excited Nonlinear Systems Subjected to External Periodic Excitations

Volume 4: 7th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B and C ◽

10.1115/detc2009-86886 ◽

2009 ◽

Cited By ~ 1

Author(s):

Sangram Redkar ◽

S. C. Sinha

Keyword(s):

Nonlinear Systems ◽

Fundamental Solution ◽

Invariant Manifold ◽

Large Scale ◽

Order Reduction ◽

Reduced Order Model ◽

Reduced Order Models ◽

Order Model ◽

Reduced Order ◽

And Control

In this work, some techniques for order reduction of nonlinear systems with periodic coefficients subjected to external periodic excitations are presented. The periodicity of the linear terms is assumed to be non-commensurate with the periodicity of forcing vector. The dynamical equations of motion are transformed using the Lyapunov-Floquet (L-F) transformation such that the linear parts of the resulting equations become time-invariant while the forcing and/or nonlinearity takes the form of quasiperiodic functions. The techniques proposed here; construct a reduced order equivalent system by expressing the non-dominant states as time-varying functions of the dominant (master) states. This reduced order model preserves stability properties and is easier to analyze, simulate and control since it consists of relatively small number of states in comparison with the large scale system. Specifically, two methods are outlined to obtain the reduced order model. First approach is a straightforward application of linear method similar to the ‘Guyan reduction’, the second novel technique proposed here, utilizes the concept of ‘invariant manifolds’ for the forced problem to construct the fundamental solution. Order reduction approach based on invariant manifold technique yields unique ‘reducibility conditions’. If these ‘reducibility conditions’ are satisfied only then an accurate order reduction via ‘invariant manifold’ is possible. This approach not only yields accurate reduced order models using the fundamental solution but also explains the consequences of various ‘primary’ and ‘secondary resonances’ present in the system. One can also recover ‘resonance conditions’ associated with the fundamental solution which could be obtained via perturbation techniques by assuming weak parametric excitation. This technique is capable of handing systems with strong parametric excitations subjected to periodic and quasi-periodic forcing. These methodologies are applied to a typical problem and results for large-scale and reduced order models are compared. It is anticipated that these techniques will provide a useful tool in the analysis and control system design of large-scale parametrically excited nonlinear systems subjected to external periodic excitations.

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