scholarly journals Uncertainty Quantification of Mode Shape Variation Utilizing Multi-Level Multi-Response Gaussian Process

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
K. Zhou ◽  
J. Tang
Keyword(s):  
Gaussian Process ◽  
Uncertainty Quantification ◽  
Mode Shape ◽  
Complex Structure ◽  
Response Strategy ◽  
Direct Monte Carlo Simulation ◽  
Shape Variation ◽  
Data Set ◽  
Shape Information ◽  
Multi Level

Abstract Mode shape information plays the essential role in deciding the spatial pattern of vibratory response of a structure. The uncertainty quantification of mode shape, i.e., predicting mode shape variation when the structure is subjected to uncertainty, can provide guidance for robust design and control. Nevertheless, computational efficiency is a challenging issue. Direct Monte Carlo simulation is unlikely to be feasible especially for a complex structure with a large number of degrees-of-freedom. In this research, we develop a new probabilistic framework built upon the Gaussian process meta-modeling architecture to analyze mode shape variation. To expedite the generation of input data set for meta-model establishment, a multi-level strategy is adopted which can blend a large amount of low-fidelity data acquired from order-reduced analysis with a small amount of high-fidelity data produced by high-dimensional full finite element analysis. To take advantage of the intrinsic relation of spatial distribution of mode shape, a multi-response strategy is incorporated to predict mode shape variation at different locations simultaneously. These yield a multi-level, multi-response Gaussian process that can efficiently and accurately quantify the effect of structural uncertainty to mode shape variation. Comprehensive case studies are carried out for demonstration and validation.

Physics Based Multi-Fidelity Data Fusion for Efficient Characterization of Mode Shape Variation Under Uncertainties

2020 ◽  
Author(s):  
K. Zhou ◽  
J. Tang
Keyword(s):  
Data Fusion ◽  
Gaussian Process ◽  
Mode Shape ◽  
Response Strategy ◽  
High Fidelity ◽  
Shape Variation ◽  
Meta Model ◽  
Shape Prediction ◽  
Intrinsic Correlation ◽  
And Control

Abstract Efficient prediction of mode shape variation under uncertainties is important for design and control. While Monte Carlo simulation (MCS) is straightforward, it is computationally expensive and not feasible for complex structures with high dimensionalities. To address this issue, in this study we develop a multi-fidelity data fusion approach with an enhanced Gaussian process (GP) architecture to evaluate mode shape variation. Since the process to acquire high-fidelity data from full-scale physical model usually is costly, we involve an order-reduced model to rapidly generate a relatively large amount of low-fidelity data. Combining these with a small amount of high-fidelity data altogether, we can establish a Gaussian process meta-model and use it for efficient model shape prediction. This enhanced meta-model allows one to capture the intrinsic correlation of model shape amplitudes at different locations by incorporating a multi-response strategy. Comprehensive case studies are performed for methodology validation.

INVERSE UNCERTAINTY QUANTIFICATION OF A CELL MODEL USING A GAUSSIAN PROCESS METAMODEL

2020 ◽  
Vol 10 (4) ◽  
pp. 333-349
Author(s):  
Kevin de Vries ◽  
Anna Nikishova ◽  
Benjamin Czaja ◽  
Gábor Závodszky ◽  
Alfons G. Hoekstra
Keyword(s):  
Gaussian Process ◽  
Uncertainty Quantification ◽  
Cell Model ◽  
A Cell

Exchange Spin Coupling from Gaussian Process Regression

2020 ◽  
Author(s):  
Marc Philipp Bahlke ◽  
Natnael Mogos ◽  
Jonny Proppe ◽  
Carmen Herrmann
Keyword(s):  
Machine Learning ◽  
Gaussian Process ◽  
Gaussian Process Regression ◽  
Molecular Magnets ◽  
Molecular Structures ◽  
Spin Coupling ◽  
Structure Property ◽  
Data Set ◽  
Uncertainty Estimates

Heisenberg exchange spin coupling between metal centers is essential for describing and understanding the electronic structure of many molecular catalysts, metalloenzymes, and molecular magnets for potential application in information technology. We explore the machine-learnability of exchange spin coupling, which has not been studied yet. We employ Gaussian process regression since it can potentially deal with small training sets (as likely associated with the rather complex molecular structures required for exploring spin coupling) and since it provides uncertainty estimates (“error bars”) along with predicted values. We compare a range of descriptors and kernels for 257 small dicopper complexes and find that a simple descriptor based on chemical intuition, consisting only of copper-bridge angles and copper-copper distances, clearly outperforms several more sophisticated descriptors when it comes to extrapolating towards larger experimentally relevant complexes. Exchange spin coupling is similarly easy to learn as the polarizability, while learning dipole moments is much harder. The strength of the sophisticated descriptors lies in their ability to linearize structure-property relationships, to the point that a simple linear ridge regression performs just as well as the kernel-based machine-learning model for our small dicopper data set. The superior extrapolation performance of the simple descriptor is unique to exchange spin coupling, reinforcing the crucial role of choosing a suitable descriptor, and highlighting the interesting question of the role of chemical intuition vs. systematic or automated selection of features for machine learning in chemistry and material science.

scholarly journals A Multiple and Multi-Level Substructure Method for the Dynamics of Complex Structures

2021 ◽  
Vol 11 (12) ◽  
pp. 5570
Author(s):  
Binbin Wang ◽  
Jingze Liu ◽  
Zhifu Cao ◽  
Dahai Zhang ◽  
Dong Jiang
Keyword(s):  
Structural Characteristics ◽  
Complex Structure ◽  
Complex Structures ◽  
System Matrix ◽  
Substructure Method ◽  
Residual Structure ◽  
The Matrix ◽  
Multi Level ◽  
Fixed Interface ◽  
Selection Of

Based on the fixed interface component mode synthesis, a multiple and multi-level substructure method for the modeling of complex structures is proposed in this paper. Firstly, the residual structure is selected according to the structural characteristics of the assembled complex structure. Secondly, according to the assembly relationship, the parts assembled with the residual structure are divided into a group of substructures, which are named the first-level substructure, the parts assembled with the first-level substructure are divided into a second-level substructure, and consequently the multi-level substructure model is established. Next, the substructures are dynamically condensed and assembled on the boundary of the residual structure. Finally, the substructure system matrix, which is replicated from the matrix of repeated physical geometry, is obtained by preserving the main modes and the constrained modes and the system matrix of the last level of the substructure is assembled to the upper level of the substructure, one level up, until it is assembled in the residual structure. In this paper, an assembly structure with three panels and a gear box is adopted to verify the method by simulation and a rotor is used to experimentally verify the method. The results show that the proposed multiple and multi-level substructure modeling method is not unique to the selection of residual structures, and different classification methods do not affect the calculation accuracy. The selection of 50% external nodes can further improve the analysis efficiency while ensuring the calculation accuracy.

Abstiegserfahrungen in der Kommune und der Aufstieg Unabhängiger Wählergemeinschaften. Neue Befunde aus einem Mehrebenen-Kommunalwahlpanel

2021 ◽  
Vol 52 (1) ◽  
pp. 59-77
Author(s):  
Christina-Marie Juen ◽  
Markus Tepe ◽  
Michael Jankowski
Keyword(s):  
Panel Data ◽  
Voter Turnout ◽  
Party System ◽  
Local Politics ◽  
Tax Revenue ◽  
Data Set ◽  
Political Fragmentation ◽  
Electoral Success ◽  
Party Positions ◽  
Multi Level

In Germany, Independent Local Lists (UWG) have become an integral part of local politics in recent decades . Despite their growing political importance, the reasons for their electoral rise have hardly been researched . Recent studies argue that Independent Local Lists pursue anti-party positions, which makes them attractive to voters who are dissatisfied with the party system . Assuming that a decline of confidence in established parties corresponds with the experience of local deprivation, this contribution uses a multi-level panel data set to investigate how socio-economic (emigration, aging, declining tax revenue) and political­cultural (turnout, fragmentation) deprivation processes affect the electoral success of Inde­pendent Local Lists . The empirical findings suggest that Independent Local Lists are more successful in municipalities where voter turnout has fallen and political fragmentation has increased .

Uncertainty Quantification in Predicting Behaviour of Rubber-Like Materials in Uni-Axial Loading

2020 ◽  
Author(s):  
Aref Ghaderi ◽  
Vahid Morovati ◽  
Pouyan Nasiri ◽  
Roozbeh Dargazany
Keyword(s):  
Uncertainty Quantification ◽  
Mechanical Response ◽  
Pure Shear ◽  
Constitutive Models ◽  
Material Behavior ◽  
Elastic Behavior ◽  
Deterministic Models ◽  
Data Set ◽  
Material Parameters ◽  
Axial Extension

Abstract Material parameters related to deterministic models can have different values due to variation of experiments outcome. From a mathematical point of view, probabilistic modeling can improve this problem. It means that material parameters of constitutive models can be characterized as random variables with a probability distribution. To this end, we propose a constitutive models of rubber-like materials based on uncertainty quantification (UQ) approach. UQ reduces uncertainties in both computational and real-world applications. Constitutive models in elastomers play a crucial role in both science and industry due to their unique hyper-elastic behavior under different loading conditions (uni-axial extension, biaxial, or pure shear). Here our goal is to model the uncertainty in constitutive models of elastomers, and accordingly, identify sensitive parameters that we highly contribute to model uncertainty and error. Modern UQ models can be implemented to use the physics of the problem compared to black-box machine learning approaches that uses data only. In this research, we propagate uncertainty through the model, characterize sensitivity of material behavior to show the importance of each parameter for uncertainty reduction. To this end, we utilized Bayesian rules to develop a model considering uncertainty in the mechanical response of elastomers. As an important assumption, we believe that our measurements are around the model prediction, but it is contaminated by Gaussian noise. We can make the noise by maximizing the posterior. The uni-axial extension experimental data set is used to calibrate the model and propagate uncertainty in this research.

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