scholarly journals Geometry of error amplification in solving the Prony system with near-colliding nodes

2020 ◽  
Vol 90 (327) ◽  
pp. 267-302 ◽  
Author(s):  
Andrey Akinshin ◽  
Gil Goldman ◽  
Yosef Yomdin
Keyword(s):  
Error Amplification

Discretization of Dynamic Loading in Time History Analysis

2013 ◽  
Vol 30 (1) ◽  
pp. 57-65
Author(s):  
S.-Y. Chang
Keyword(s):  
Dynamic Loading ◽  
Amplification Factor ◽  
Integration Method ◽  
Time History ◽  
Discretization Error ◽  
Amplitude Error ◽  
History Analysis ◽  
Asymptotic Constant ◽  
Error Amplification ◽  
General Step

ABSTRACTAlthough the numerical properties of a step-by-step integration method can be evaluated based on the currently available techniques, there is still lack of a technique for evaluating its capability to capture dynamic loading. In this work, the amplitude error caused by the step discretization error is identified and the correlation between the relative amplitude error and relative step discretization error is analytically established. As a result, it is thoroughly confirmed that the asymptotic constant of the discretization error amplification factor for the displacement response to a cosine loading can be considered as an indicator of the capability to capture dynamic loading for a general step-by-step integration method.

scholarly journals Quantitative View on the Processes Governing the Upscale Error Growth up to the Planetary Scale Using a Stochastic Convection Scheme

2019 ◽  
Vol 147 (5) ◽  
pp. 1713-1731 ◽  
Author(s):  
Marlene Baumgart ◽  
Paolo Ghinassi ◽  
Volkmar Wirth ◽  
Tobias Selz ◽  
George C. Craig ◽  
...  
Keyword(s):  
Large Error ◽  
Error Growth ◽  
Atmospheric Conditions ◽  
Convection Scheme ◽  
Planetary Scale ◽  
Divergent Wind ◽  
Tropopause Region ◽  
Error Amplification ◽  
Forecast Models ◽  
Design Representations

Abstract Two diagnostics based on potential vorticity and the envelope of Rossby waves are used to investigate upscale error growth from a dynamical perspective. The diagnostics are applied to several cases of global, real-case ensemble simulations, in which the only difference between the ensemble members lies in the random seed of the stochastic convection scheme. Based on a tendency equation for the enstrophy error, the relative importance of individual processes to enstrophy-error growth near the tropopause is quantified. After the enstrophy error is saturated on the synoptic scale, the envelope diagnostic is used to investigate error growth up to the planetary scale. The diagnostics reveal distinct stages of the error growth: in the first 12 h, error growth is dominated by differences in the convection scheme. Differences in the upper-tropospheric divergent wind then project these diabatic errors into the tropopause region (day 0.5–2). The subsequent error growth (day 2–14.5) is governed by differences in the nonlinear near-tropopause dynamics. A fourth stage of the error growth is found up to 18 days when the envelope diagnostic indicates error growth from the synoptic up to the planetary scale. Previous ideas of the multiscale nature of upscale error growth are confirmed in general. However, a novel interpretation of the governing processes is provided. The insight obtained into the dynamics of upscale error growth may help to design representations of uncertainty in operational forecast models and to identify atmospheric conditions that are intrinsically prone to large error amplification.

Focused inversion of vertical radar profile (VRP) traveltime data

Geophysics ◽  
2012 ◽  
Vol 77 (1) ◽  
pp. H9-H18 ◽  
Author(s):  
Giulio Vignoli ◽  
Rita Deiana ◽  
Giorgio Cassiani
Keyword(s):  
Inverse Problem ◽  
Physical Properties ◽  
Reference Model ◽  
A Priori ◽  
S Wave ◽  
Compact Structure ◽  
Arrival Times ◽  
Minimum Support ◽  
Error Amplification ◽  
Zero Offset

The reconstruction of the GPR velocity vertical profile from vertical radar profile (VRP) traveltime data is a problem with a finite number of measurements and imprecise data, analogous to similar seismic techniques, such as the shallow down-hole test used for S-wave velocity profiling or the vertical seismic profiling (VSP) commonly used in deeper exploration. The uncertainty in data accuracy and the error amplification inherent in deriving velocity estimates from gradients of arrival times make this an example of an ill-posed inverse problem. In the framework of Tikhonov regularization theory, ill-posedness can be tackled by introducing a regularizing functional (stabilizer). The role of this functional is to stabilize the numerical solution by incorporating the appropriate a priori assumptions about the geometrical and/or physical properties of the solution. One of these assumptions could be the existence of sharp boundaries separating rocks with different physical properties. We apply a method based on the minimum support stabilizer to the VRP traveltime inverse problem. This stabilizer makes it possible to produce more accurate profiles of geological targets with compact structure. We compare more traditional inversion results with our proposed compact reconstructions. Using synthetic examples, we demonstrate that the minimum support stabilizer allows an improved recovery of the profile shape and velocity values of blocky targets. We also study the stabilizer behavior with respect to different noise levels and different choices of the reference model. The proposed approach is then applied to real cases where VPRs have been used to derive moisture content profiles as a function of depth. In these real cases, the derived sharper profiles are consistent with other evidence, such as GPR zero-offset profiles, GPR reflections and known locations of the water table.

scholarly journals Neural circuits activated by error amplification and haptic guidance training techniques during performance of a timing-based motor task by healthy individuals

2018 ◽  
Vol 236 (11) ◽  
pp. 3085-3099 ◽  
Author(s):  
Marie-Hélène Milot ◽  
Laura Marchal-Crespo ◽  
Louis-David Beaulieu ◽  
David J. Reinkensmeyer ◽  
Steven C. Cramer
Keyword(s):  
Neural Circuits ◽  
Motor Task ◽  
Haptic Guidance ◽  
Healthy Individuals ◽  
Training Techniques ◽  
Error Amplification

scholarly journals Cortical reorganization to improve dynamic balance control with error amplification feedback

2022 ◽  
Vol 19 (1) ◽  
Author(s):  
Yi-Ching Chen ◽  
Yi-Ying Tsai ◽  
Gwo-Ching Chang ◽  
Ing-Shiou Hwang
Keyword(s):  
Visual Feedback ◽  
Neural Control ◽  
Balance Control ◽  
Dynamic Balance ◽  
Cortical Reorganization ◽  
Phase Lag ◽  
Behavioral Strategies ◽  
Beta Band ◽  
Error Amplification ◽  
The Right

Abstract Background Error amplification (EA), virtually magnify task errors in visual feedback, is a potential neurocognitive approach to facilitate motor performance. With regional activities and inter-regional connectivity of electroencephalography (EEG), this study investigated underlying cortical mechanisms associated with improvement of postural balance using EA. Methods Eighteen healthy young participants maintained postural stability on a stabilometer, guided by two visual feedbacks (error amplification (EA) vs. real error (RE)), while stabilometer plate movement and scalp EEG were recorded. Plate dynamics, including root mean square (RMS), sample entropy (SampEn), and mean frequency (MF) were used to characterize behavioral strategies. Regional cortical activity and inter-regional connectivity of EEG sub-bands were characterized to infer neural control with relative power and phase-lag index (PLI), respectively. Results In contrast to RE, EA magnified the errors in the visual feedback to twice its size during stabilometer stance. The results showed that EA led to smaller RMS of postural fluctuations with greater SampEn and MF than RE did. Compared with RE, EA altered cortical organizations with greater regional powers in the mid-frontal cluster (theta, 4–7 Hz), occipital cluster (alpha, 8–12 Hz), and left temporal cluster (beta, 13–35 Hz). In terms of the phase-lag index of EEG between electrode pairs, EA significantly reduced long-range prefrontal-parietal and prefrontal-occipital connectivity of the alpha/beta bands, and the right tempo-parietal connectivity of the theta/alpha bands. Alternatively, EA augmented the fronto-centro-parietal connectivity of the theta/alpha bands, along with the right temporo-frontal and temporo-parietal connectivity of the beta band. Conclusion EA alters postural strategies to improve stance stability on a stabilometer with visual feedback, attributable to enhanced error processing and attentional release for target localization. This study provides supporting neural correlates for the use of virtual reality with EA during balance training.

Error amplification in capillary viscometry of power law fluids with slip

2020 ◽  
Vol 91 ◽  
pp. 106816 ◽  
Author(s):  
Lorenzo Malagutti ◽  
Francesco Mollica ◽  
Valentina Mazzanti
Keyword(s):  
Power Law ◽  
Power Law Fluids ◽  
Error Amplification
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