Stochastic Superparameterization and Multiscale Filtering of Turbulent Tracers

2017 ◽  
Vol 15 (1) ◽  
pp. 215-234 ◽  
Author(s):  
Yoonsang Lee ◽  
Andrew J. Majda ◽  
Di Qi
Keyword(s):  
Multiscale Filtering

scholarly journals Integrated Multiscale Latent Variable Regression and Application to Distillation Columns

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Muddu Madakyaru ◽  
Mohamed N. Nounou ◽  
Hazem N. Nounou
Keyword(s):  
Feature Extraction ◽  
Latent Variable ◽  
Prediction Accuracy ◽  
Distillation Column ◽  
Selection Criterion ◽  
Process Data ◽  
Distillation Columns ◽  
Latent Variable Regression ◽  
Multiscale Filtering ◽  
Modeling Algorithm

Proper control of distillation columns requires estimating some key variables that are challenging to measure online (such as compositions), which are usually estimated using inferential models. Commonly used inferential models include latent variable regression (LVR) techniques, such as principal component regression (PCR), partial least squares (PLS), and regularized canonical correlation analysis (RCCA). Unfortunately, measured practical data are usually contaminated with errors, which degrade the prediction abilities of inferential models. Therefore, noisy measurements need to be filtered to enhance the prediction accuracy of these models. Multiscale filtering has been shown to be a powerful feature extraction tool. In this work, the advantages of multiscale filtering are utilized to enhance the prediction accuracy of LVR models by developing an integrated multiscale LVR (IMSLVR) modeling algorithm that integrates modeling and feature extraction. The idea behind the IMSLVR modeling algorithm is to filter the process data at different decomposition levels, model the filtered data from each level, and then select the LVR model that optimizes a model selection criterion. The performance of the developed IMSLVR algorithm is illustrated using three examples, one using synthetic data, one using simulated distillation column data, and one using experimental packed bed distillation column data. All examples clearly demonstrate the effectiveness of the IMSLVR algorithm over the conventional methods.

A Multiscale Filtering Explanation of Gradient Induction and Remote Brightness Induction Effects: A Reply to Logvinenko (2003)

Perception ◽  
2005 ◽  
Vol 34 (7) ◽  
pp. 793-802 ◽  
Author(s):  
Barbara Blakeslee ◽  
Mark E McCourt
Keyword(s):  
Strong Evidence ◽  
Test Strip ◽  
Spatial Filter ◽  
Brightness Variation ◽  
Sine Wave ◽  
Difference Of Gaussians ◽  
Limited Class ◽  
Homogeneous Test ◽  
Multiscale Filtering ◽  
Filtering Approach

Grating induction is a brightness effect in which a counterphase spatial brightness variation (a grating) is induced in a homogeneous test strip that is surrounded by an inducing luminance grating (McCourt, 1982 Vision Research22 119–134). Moulden and Kingdom (1991 Vision Research31 1999–2008) introduced an interesting variant of grating induction (sometimes referred to as gradient induction) in which multiple strips of either a linear luminance ramp or a sine-wave grating were interlaced with strips of homogeneous luminance. We (Blakeslee and McCourt, 1999 Vision Research39 4361–4377) demonstrated that a simple multiscale filtering explanation could account for grating induction. Recently, however, Logvinenko (2003 Perception32 621–626) presented several arguments impugning the adequacy of spatial filtering approaches to understanding brightness induction in gradient induction stimuli. We propose that Logvinenko's arguments apply only to a limited class of filtering models, specifically those which employ only a single spatial filter. To test this hypothesis we modeled gradient induction stimuli as a function of inducing contrast, as well as Logvinenko's (2003) remote induction stimulus, using our multiscale oriented difference-of-Gaussians (ODOG) model (Blakeslee and McCourt 1999). The ODOG model successfully predicts the appearance of the inducing strips and the homogeneous test strips in the gradient induction stimuli and the appearance of the test patches in the remote induction stimuli. These results refute Logvinenko's (2003) claims, and we interpret them as providing strong evidence for a multiscale filtering approach to understanding both gradient induction and remote brightness induction effects.

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