Mixed-Dimensional Model Analysis Under Dimension Reduction Error Control

2012 ◽  
Author(s):  
Jianguo Tang ◽  
Shuming Gao ◽  
Ming Li ◽  
Feiwei Qin
Keyword(s):  
Dimension Reduction ◽  
Error Control ◽  
Final Analysis ◽  
Original Model ◽  
Dimensional Model ◽  
Evaluation Indicator ◽  
Engineering Models ◽  
Analysis Error ◽  
Reduction Error ◽  
Analysis Errors

In order to conduct engineering analysis efficiently, complex CAD model is generally idealized by dimension reduction of its local thin regions into mid-surfaces, which results in a mixed-dimensional model. However, such dimension reduction inevitably induces analysis errors when plate or shell theory applied to the mixed-dimensional model. In this paper, an evaluation indicator is proposed for estimating analysis error induced by dimension reduction of a original model into mixed-dimensional model and used to control the analysis results of the mixed-dimensional model with given accuracy. The evaluation indicator is defined as the stress difference on the coupling interface between the mixed-dimensional model and the original model. When the mixed-dimensional model is analyzed, p-version solid elements were generated by offsetting the shell nodes in the thickness direction. Moreover, element stiffness matrix, boundary conditions and material properties can be extracted from the analysis results and reused for the indicator computation. Displacements of the mixed-dimensional model are input as initial value to iterative solver to accelerate the computation. When the indicator is below the accuracy, final analysis can be proceeded with p-adaptivity in the thin regions. The hierarchical shape function for p-version solid elements ensures the efficiency of the error estimation and the reliability of the final analysis. The robustness of the evaluation indicator and computational efficiency for final analysis are illustrated by experiments on engineering models.

A VECTOR-LIKE LARGE N APPROACH TO ZERO-DIMENSIONAL SU(2) MATRIX MODELS

1993 ◽  
Vol 08 (23) ◽  
pp. 4175-4192 ◽  
Author(s):  
JOĀO P. RODRIGUES ◽  
ALEXANDER WELTE
Keyword(s):  
Matrix Models ◽  
Original Model ◽  
Feynman Diagrams ◽  
Dimensional Model ◽  
Large N

The action of an SU(2) multimatrix model can always be rewritten as that of an SO(3) multivector model. In the context of a zero-dimensional model, we argue that all symmetry invariants can be expressed in terms of O(3) invariants and develop a systematic, vector-like [Formula: see text] approximation. This approximation has no interpretation in terms of subsets of Feynman diagrams of the original model.

scholarly journals Non-Gaussian statistics in global atmospheric dynamics: a study with a 10 240-member ensemble Kalman filter using an intermediate AGCM

2018 ◽  
Author(s):  
Keiichi Kondo ◽  
Takemasa Miyoshi
Keyword(s):  
Kalman Filter ◽  
General Circulation ◽  
Circulation Model ◽  
Tropical Regions ◽  
Highly Nonlinear ◽  
Gaussian Statistics ◽  
Ensemble Transform Kalman Filter ◽  
Analysis Error ◽  
Non Gaussian ◽  
Analysis Errors

Abstract. We previously performed local ensemble transform Kalman filter experiments with up to 10 240 ensemble members using an intermediate atmospheric general circulation model. While the previous study focused on the localization impact on the analysis accuracy, the present study focuses on the probability density functions (PDFs) represented by the 10 240-member ensemble. The 10 240-member ensemble can resolve the detailed structures of the PDFs and indicates that the non-Gaussian PDF is caused by multimodality and outliers. The results show that the spatial patterns of the analysis errors correspond well with the non-Gaussianity. While the outliers appear randomly, large multimodality corresponds well with large analysis error, mainly in the tropical regions where highly nonlinear convective processes appear frequently. Therefore, we further investigate the lifecycle of multimodal PDFs, and show that the multimodal PDFs are generated by the on-off switch of convective parameterization and disappear naturally. Sensitivity to the ensemble size suggests that approximately 1000 ensemble members be necessary to capture the detailed structures of the non-Gaussian PDF.

scholarly journals The Characteristics of Key Analysis Errors. Part I: Dynamical Balance and Comparison with Observations

2007 ◽  
Vol 135 (2) ◽  
pp. 249-266 ◽  
Author(s):  
Jean-François Caron ◽  
M. K. Yau ◽  
Stéphane Laroche ◽  
Peter Zwack
Keyword(s):  
Forecast Error ◽  
Forecast Errors ◽  
Control Analysis ◽  
Initial Condition ◽  
Initial State ◽  
Mass Correction ◽  
Current Algorithm ◽  
Dynamical Balance ◽  
Analysis Error ◽  
Analysis Errors

Abstract The characteristics of the initial corrections obtained from the Canadian Meteorological Centre (CMC) energy-norm-based key analysis error algorithm that minimizes short-range (24 h) forecast errors were investigated for four specific CMC operational analyses. The results show that both the rotational and the divergent components of the initial corrections are strongly out of balance. Some dispersive modes are also present in the mass component of the initial corrections. The results from one experiment where the initial state errors were known suggest that the current algorithm always selects a set of unbalanced initial corrections with more mass correction than wind correction, regardless of the characteristics of the real initial condition errors. Comparison with observational data showed that the corrected analysis is systematically farther away from the observations than the control analysis even in large forecast error events where most of the forecast errors are believed to have originated from errors in the initial state.

Hybrid multiplicative dimension reduction method for uncertainty analysis of engineering structures

2020 ◽  
pp. 1748006X2092997
Author(s):  
Haihe Li ◽  
Pan Wang ◽  
Qi Chang ◽  
Changcong Zhou ◽  
Zhufeng Yue
Keyword(s):  
Uncertainty Analysis ◽  
Dimension Reduction ◽  
Reduction Method ◽  
High Dimensional ◽  
Sensitivity Index ◽  
Dimension Reduction Method ◽  
Engineering Structures ◽  
High Order Derivative ◽  
Engineering Models ◽  
Complex Engineering

For uncertainty analysis of high-dimensional complex engineering problems, this article proposes a hybrid multiplicative dimension reduction method based on the existent multiplicative dimension reduction method. It uses the multiplicative dimension reduction method to approximate the original high-dimensional performance function which is sufficiently smooth and has a small high-order derivative as the product of a series of one-dimensional functions, and then uses this approximation to calculate the statistical moments of the function. Then the variance-based global sensitivity index is employed to identify the important variables, and the identified important variables are subjected to bivariate decomposition approximation. Combined with the univariate multiplicative dimension reduction method, the hybrid decomposition approximation is obtained. Compared with the existing method, the proposed method is more accurate than the univariate decomposition approximation when used for uncertainty analysis of engineering models and needs less computational efforts than the bivariate decomposition. In the end, a numerical example and two engineering applications are tested to verify the effectiveness of the proposed method.

scholarly journals The Characteristics of Key Analysis Errors. Part II: The Importance of the PV Corrections and the Impact of Balance

2007 ◽  
Vol 135 (2) ◽  
pp. 267-280 ◽  
Author(s):  
Jean-François Caron ◽  
M. K. Yau ◽  
Stéphane Laroche ◽  
Peter Zwack
Keyword(s):  
Short Range ◽  
Vertical Motion ◽  
Forecast Errors ◽  
Divergent Part ◽  
Essential Information ◽  
Original Analysis ◽  
Analysis Error ◽  
Motion Corrections ◽  
The Impact ◽  
Analysis Errors

Abstract This study examines a few approaches to isolate the balanced component of the initial corrections from the Canadian Meteorological Centre energy-norm-based key analysis error algorithm, in an attempt to capture the part of the key analysis errors responsible for short-range forecast errors. The best results were obtained with the nonlinear balance potential vorticity (PV) inversion technique. It was shown that the PV component of the initial corrections contains the essential information for reducing short-range forecast errors. The remaining imbalance part of the initial corrections does not grow in time and does not contribute to the improvement of the forecast. The removal of the imbalance part of the initial corrections makes the corrected analysis slightly closer to the observations, but remains systematically farther away as compared with the original analysis. Thus the balanced part of the key analysis errors cannot justifiably be associated to analysis errors. A methodology to balance the divergent part of the initial corrections, which reduces significantly the spinup in the vertical motion corrections, is also presented. Finally, in light of the results presented in this paper, some recommendations to improve the key analysis error algorithm are proposed.

Dimension Reduction of Biological Neuron Models by Artificial Neural Networks

1994 ◽  
Vol 6 (4) ◽  
pp. 696-717 ◽  
Author(s):  
Kenji Doya ◽  
Allen I. Selverston
Keyword(s):  
Dimension Reduction ◽  
Three Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Neuron Models ◽  
Neural Network Approach ◽  
Bursting Neuron ◽  
Biological Neuron ◽  
Artificial Neural ◽  
Artificial Neural Network Approach

An artificial neural network approach to dimension reduction of dynamical systems is proposed and applied to conductance-based neuron models. Networks with bottleneck layers of continuous-time dynamical units could make a two-dimensional model from the trajectories of the Hodgkin-Huxley model and a three-dimensional model from the trajectories of a six-dimensional bursting neuron model. Nullcline analysis of these reduced models revealed the bifurcations of the dynamical system underlying firing and bursting behaviors.

scholarly journals CLRM-12. HYBRID DESIGNS FOR USING EXTERNAL CONTROLS IN PHASE 3 GLIOBLASTOMA TRIALS

2021 ◽  
Vol 3 (Supplement_4) ◽  
pp. iv3-iv3
Author(s):  
Mei-Yin Polley ◽  
Daniel Schwartz ◽  
James Dignam
Keyword(s):  
Error Control ◽  
Final Analysis ◽  
Adaptive Designs ◽  
External Control ◽  
Operating Characteristics ◽  
Accelerate Phase ◽  
High Quality ◽  
Phase 3 ◽  
Recent Phase ◽  
Therapy Development

Abstract While recent Phase 3 glioblastoma (GBM) trials have failed to establish novel therapies, they potentially provide a high-quality source of external control patients treated with temozolomide. We consider hybrid two-stage adaptive designs that leverage these external controls to safely accelerate Phase 3 GBM trials. The basic strategy is that first patients are randomized 1:1 between the control and experimental arms, then an interim check measures similarity between the trial's control patients and potential external controls, and finally if this interim similarity is high the randomization ratio is changed accordingly and the external controls are used in the final analysis. An extensive simulation study is conducted to assess operating characteristics and we discuss when these hybrid designs can accelerate GBM therapy development while maintaining strict error control.

scholarly journals The Characteristics of Key Analysis Errors. Part III: A Diagnosis of Their Evolution

2007 ◽  
Vol 135 (7) ◽  
pp. 2754-2777 ◽  
Author(s):  
Jean-François Caron ◽  
M. K. Yau ◽  
Stéphane Laroche
Keyword(s):  
Level Structure ◽  
Potential Temperature ◽  
Initial Time ◽  
Forecast Errors ◽  
Diagnostic Study ◽  
Low Level ◽  
Diabatic Processes ◽  
Upper Level ◽  
Analysis Error ◽  
Analysis Errors

Abstract This paper presents a diagnostic study of the evolution of initial corrections obtained from the key analysis error algorithm that minimizes the short-range (24 h) forecast errors for four specific events poorly forecasted over the eastern part of North America. A potential vorticity (PV) perspective is employed. It is shown that the modification to the low-level structure at the initial time is mainly attributed to the modification of the low-level PV distribution, while changes in the upper-level structure are attributed to the modification of the upper-level PV distribution. The low-level corrections grow mainly through background surface potential temperature advection by the wind corrections attributable to the interior PV corrections. Changes in the diabatic processes and the vertical alignment of low-level PV corrections by differential PV advection also increase the magnitude of the low-level corrections with time. The upper-level corrections grow by advection of background PV from wind corrections. However, the cause of these latter wind corrections responsible for upper-level background PV advection varies from case to case. An investigation of the relative importance of the low-level and of the upper-level initial corrections to produce the final-time corrections also reveals strong variability between cases. Finally, comparison of two cases in which the key analysis errors propagate vertically with two others without significant vertical propagation shows how the relative position of the key analysis errors with respect to the structure of the background flow can influence the evolution of the initial corrections.

Sign in / Sign up

Export Citation Format

Share Document