Nonlinear Transient Localization and Beat Phenomena Due to Backlash in a Coupled Flexible System

2000 ◽  
Vol 123 (1) ◽  
pp. 36-44 ◽  
Author(s):  
Xianghong Ma ◽  
Alexander F. Vakakis
Keyword(s):  
Nonlinear Models ◽  
Order Reduction ◽  
Nonlinear Effects ◽  
Computationally Efficient ◽  
Nonlinear Localization ◽  
Flexible System ◽  
Energy Transfers ◽  
System Reconstruction ◽  
Nonlinear Transient ◽  
Low Dimensional

Transient nonlinear localization and beat phenomena are studied in a system of two rods coupled with a nonlinear backlash spring. The method of Karhunen-Loeve (K-L) decomposition is used to reduce the order of the dynamics, and to study nonlinear effects by considering energy transfers between leading K-L modes. The computed K-L modes are used to discretize the governing partial differential equations, thus creating accurate and computationally efficient low-dimensional nonlinear models of the system. Reconstruction of transient nonlinear responses using these low dimensional models reveals the accuracy of the order reduction. Poincare´ maps are utilized to study the nonlinear localization and beat phenomena caused by the clearance connecting the coupled rods.

Nonlinear Transient Localization and Beat Phenomena due to Backlash in a Coupled Flexible System

2001 ◽  
Author(s):  
Xianghong Ma ◽  
Alexander F. Vakakis
Keyword(s):  
Nonlinear Models ◽  
Order Reduction ◽  
Nonlinear Effects ◽  
Computationally Efficient ◽  
Nonlinear Localization ◽  
Flexible System ◽  
Energy Transfers ◽  
System Reconstruction ◽  
Nonlinear Transient ◽  
Low Dimensional

Abstract Transient nonlinear localization and beat phenomena are studied in a system of two rods coupled with a nonlinear backlash spring. The method of Karhunen-Loeve (K-L) decomposition is used to reduce the order of the dynamics, and to study nonlinear effects by considering energy transfers between leading K-L modes. The computed K-L modes are used to discretize the governing partial differential equations, thus creating accurate and computationally efficient low-dimensional nonlinear models of the system. Reconstruction of transient nonlinear responses using these low dimensional models reveals the accuracy of the order reduction. Poincare’ maps are utilized to study the nonlinear localization and beat phenomena caused by the clearance connecting the coupled rods.

Nonlinear Transient Localization and Low Dimensional Models of a Flexible System With a Clearance

1999 ◽  
Author(s):  
Xianghong Ma ◽  
Alexander F. Vakakis
Keyword(s):  
Nonlinear Models ◽  
Order Reduction ◽  
Nonlinear Effects ◽  
Computationally Efficient ◽  
Nonlinear Localization ◽  
Flexible System ◽  
Energy Transfers ◽  
Nonlinear Transient ◽  
Dimensional Models ◽  
Low Dimensional

Abstract Transient nonlinear localization in a system of two rods coupled with a nonlinear backlash spring is studied in this work. The method of Karhunen-Loeve (K-L) decomposition is then used to reduce the order of the dynamics, and to study nonlinear effects by considering energy transfers between leading K-L modes. In addition, the computed K-L modes are used to discretize the governing partial differential equations, thus creating accurate and computationally efficient low-dimensional nonlinear models of the system. Reconstructions of transient nonlinear responses using these low dimensional models reveals the accuracy of the order reduction.

Uncertainty quantification/propagation in nonlinear models

2017 ◽  
Vol 34 (4) ◽  
pp. 1082-1106 ◽  
Author(s):  
Khaoula Chikhaoui ◽  
Noureddine Bouhaddi ◽  
Najib Kacem ◽  
Mohamed Guedri ◽  
Mohamed Soula
Keyword(s):  
Nonlinear Models ◽  
Uncertainty Propagation ◽  
Latin Hypercube Sampling ◽  
Nonlinear Effects ◽  
Significant Loss ◽  
Computational Time ◽  
Parametric Uncertainties ◽  
Computationally Efficient ◽  
Content Type ◽  
Stochastic Parameters

Purpose The purpose of this paper is to develop robust metamodels, which allow propagating parametric uncertainties, in the presence of localized nonlinearities, with reduced cost and without significant loss of accuracy. Design/methodology/approach The proposed metamodels combine the generalized polynomial chaos expansion (gPCE) for the uncertainty propagation and reduced order models (ROMs). Based on the computation of deterministic responses, the gPCE requires prohibitive computational time for large-size finite element models, large number of uncertain parameters and presence of nonlinearities. To overcome this issue, a first metamodel is created by combining the gPCE and a ROM based on the enrichment of the truncated Ritz basis using static residuals taking into account the stochastic and nonlinear effects. The extension to the Craig–Bampton approach leads to a second metamodel. Findings Implementing the metamodels to approximate the time responses of a frame and a coupled micro-beams structure containing localized nonlinearities and stochastic parameters permits to significantly reduce computation cost with acceptable loss of accuracy, with respect to the reference Latin Hypercube Sampling method. Originality/value The proposed combination of the gPCE and the ROMs leads to a computationally efficient and accurate tool for robust design in the presence of parametric uncertainties and localized nonlinearities.

scholarly journals Eight Simple Guidelines for Improved Understanding of Transformations and Nonlinear Effects

2021 ◽  
pp. 109442812199190
Author(s):  
Mikko Rönkkö ◽  
Eero Aalto ◽  
Henni Tenhunen ◽  
Miguel I. Aguirre-Urreta
Keyword(s):  
Generalized Linear Model ◽  
Functional Form ◽  
Nonlinear Models ◽  
Nonlinear Effects ◽  
Recent Past ◽  
Organizational Research ◽  
Common Practices ◽  
Individual Variables ◽  
The Individual ◽  
The Relationship

Transforming variables before analysis or applying a transformation as a part of a generalized linear model are common practices in organizational research. Several methodological articles addressing the topic, either directly or indirectly, have been published in the recent past. In this article, we point out a few misconceptions about transformations and propose a set of eight simple guidelines for addressing them. Our main argument is that transformations should not be chosen based on the nature or distribution of the individual variables but based on the functional form of the relationship between two or more variables that is expected from theory or discovered empirically. Building on a systematic review of six leading management journals, we point to several ways the specification and interpretation of nonlinear models can be improved.

scholarly journals Feature-based data assimilation in geophysics

2017 ◽  
Author(s):  
Matthias Morzfeld ◽  
Jesse Adams ◽  
Spencer Lunderman ◽  
Rafael Orozco
Keyword(s):  
Computational Models ◽  
Chaotic Systems ◽  
Efficient Solutions ◽  
Effective Dimension ◽  
Dimensional Model ◽  
Computationally Efficient ◽  
Fundamental Understanding ◽  
Feature Based ◽  
Low Dimensional ◽  
Noise Models

Abstract. Many applications in science require that computational models and data be combined. In a Bayesian framework, this is usually done by defining likelihoods based on the mismatch of model outputs and data. However, matching model outputs and data in this way can be unnecessary or impossible. For example, using large amounts of steady state data is unnecessary because these data are redundant, it is numerically difficult to assimilate data in chaotic systems, and it is often impossible to assimilate data of a complex system into a low-dimensional model. These issues can be addressed by selecting features of the data, and defining likelihoods based on the features, rather than by the usual mismatch of model output and data. Our goal is to contribute to a fundamental understanding of such a feature-based approach that allows us to assimilate selected aspects of data into models. Specifically, we explain how the feature-based approach can be interpreted as a method for reducing an effective dimension, and derive new noise models, based on perturbed observations, that lead to computationally efficient solutions. Numerical implementations of our ideas are illustrated in four examples.

scholarly journals Toward Optimality of Proper Generalised Decomposition Bases

2019 ◽  
Vol 24 (1) ◽  
pp. 30 ◽  
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.

scholarly journals Image Segmentation and Identification of Paired Antibodies in Breast Tissue

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Jimmy C. Azar ◽  
Martin Simonsson ◽  
Ewert Bengtsson ◽  
Anders Hast
Keyword(s):  
Breast Tissue ◽  
Principal Component ◽  
Feature Space ◽  
Tissue Microarrays ◽  
Specific Protein ◽  
Blue Dye ◽  
Computationally Efficient ◽  
Automated Quantification ◽  
Human Protein Atlas ◽  
Low Dimensional

Comparing staining patterns of paired antibodies designed towards a specific protein but toward different epitopes of the protein provides quality control over the binding and the antibodies’ ability to identify the target protein correctly and exclusively. We present a method for automated quantification of immunostaining patterns for antibodies in breast tissue using the Human Protein Atlas database. In such tissue, dark brown dye 3,3′-diaminobenzidine is used as an antibody-specific stain whereas the blue dye hematoxylin is used as a counterstain. The proposed method is based on clustering and relative scaling of features following principal component analysis. Our method is able (1) to accurately segment and identify staining patterns and quantify the amount of staining and (2) to detect paired antibodies by correlating the segmentation results among different cases. Moreover, the method is simple, operating in a low-dimensional feature space, and computationally efficient which makes it suitable for high-throughput processing of tissue microarrays.

scholarly journals Combined Reinforcement Learning via Abstract Representations

2019 ◽  
Vol 33 ◽  
pp. 3582-3589 ◽  
Author(s):  
Vincent Francois-Lavet ◽  
Yoshua Bengio ◽  
Doina Precup ◽  
Joelle Pineau
Keyword(s):  
Reinforcement Learning ◽  
State Space ◽  
Transfer Learning ◽  
Computationally Efficient ◽  
Dimensional Representation ◽  
Learning Methods ◽  
Model Free ◽  
Abstract Representations ◽  
Low Dimensional ◽  
New Strategies

In the quest for efficient and robust reinforcement learning methods, both model-free and model-based approaches offer advantages. In this paper we propose a new way of explicitly bridging both approaches via a shared low-dimensional learned encoding of the environment, meant to capture summarizing abstractions. We show that the modularity brought by this approach leads to good generalization while being computationally efficient, with planning happening in a smaller latent state space. In addition, this approach recovers a sufficient low-dimensional representation of the environment, which opens up new strategies for interpretable AI, exploration and transfer learning.

scholarly journals Parametric Nonlinear Model Reduction Using K-Means Clustering for Miscible Flow Simulation

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Norapon Sukuntee ◽  
Saifon Chaturantabut
Keyword(s):  
Clustering Algorithm ◽  
Interpolation Method ◽  
Flow Simulation ◽  
Order Reduction ◽  
Galerkin Projection ◽  
Parameter Domain ◽  
Miscible Flow ◽  
Multidimensional Parameter ◽  
Discrete Empirical Interpolation Method ◽  
Low Dimensional

This work considers the model order reduction approach for parametrized viscous fingering in a horizontal flow through a 2D porous media domain. A technique for constructing an optimal low-dimensional basis for a multidimensional parameter domain is introduced by combining K-means clustering with proper orthogonal decomposition (POD). In particular, we first randomly generate parameter vectors in multidimensional parameter domain of interest. Next, we perform the K-means clustering algorithm on these parameter vectors to find the centroids. POD basis is then generated from the solutions of the parametrized systems corresponding to these parameter centroids. The resulting POD basis is then used with Galerkin projection to construct reduced-order systems for various parameter vectors in the given domain together with applying the discrete empirical interpolation method (DEIM) to further reduce the computational complexity in nonlinear terms of the miscible flow model. The numerical results with varying different parameters are demonstrated to be efficient in decreasing simulation time while maintaining accuracy compared to the full-order model for various parameter values.

Bayesian analysis of longitudinal and multidimensional functional data

Biostatistics ◽  
2020 ◽  
Author(s):  
John Shamshoian ◽  
Damla Şentürk ◽  
Shafali Jeste ◽  
Donatello Telesca
Keyword(s):  
Functional Data ◽  
Observational Studies ◽  
Children With Autism ◽  
Autism Spectrum ◽  
Computationally Efficient ◽  
Modeling Framework ◽  
Simulated Environment ◽  
First Case ◽  
Low Dimensional

Summary Multi-dimensional functional data arises in numerous modern scientific experimental and observational studies. In this article, we focus on longitudinal functional data, a structured form of multidimensional functional data. Operating within a longitudinal functional framework we aim to capture low dimensional interpretable features. We propose a computationally efficient nonparametric Bayesian method to simultaneously smooth observed data, estimate conditional functional means and functional covariance surfaces. Statistical inference is based on Monte Carlo samples from the posterior measure through adaptive blocked Gibbs sampling. Several operative characteristics associated with the proposed modeling framework are assessed comparatively in a simulated environment. We illustrate the application of our work in two case studies. The first case study involves age-specific fertility collected over time for various countries. The second case study is an implicit learning experiment in children with autism spectrum disorder.

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