Robust worst-case scenarios from ensemble forecasts

To extract the most information from an ensemble forecast, users would need to consider the possible impacts of every member in the ensemble. However, not all users have the resources to do this. Many may opt to consider only the ensemble mean and possibly some measure of spread around the mean. This provides little information about potential worst-case scenarios. We explore different methods to extract worst-case scenarios from an ensemble forecast, for a given definition of severity of impact: taking the worst member of the ensemble, calculating the mean of the N worst members, and two methods that use a statistical tool known as directional component analysis (DCA).We assess the advantages and disadvantages of the four methods in terms of whether they produce spatial worst-case scenarios that are not overly sensitive to the finite size and randomness of the ensemble or small changes in the chosen geographical domain. The methods are tested on synthetic data and on temperature forecasts from ECMWF. The mean of the N worst members is more robust than the worst member, while the DCA-based patterns are more robust than either. Furthermore, if the ensemble variability is well-described by the covariance matrix, the DCA patterns have the statistical property that they are just as severe as those from the other two methods, but more likely. We conclude that the DCA approach is a tool that could be routinely applied to extract worst-case scenarios from ensemble forecasts.

Nonlinear dynamic response of seismically excited rectangular concrete liquid filled tanks

The effect of nonlinearity on behaviour of rectangular concrete tanks partially filled with water is studied. The nonlinearity in the numerical modeling of the surface liquid sloshing performance and hydrodynamic pressure initiates from unknown boundary conditions of contained liquid volume. The nonlinear simulations are performed for Time-History seismic analysis using the finite element software ABAQUS/CAE. The nonlinear results are compared with linear analytical solutions and ACI 350.3-06 code. A Paramedic study is conducted to investigate the effect of tank plan dimension, frequency content of different seismic ground motions, nature of earthquake movements, and interaction of bi-directional component of earthquake on the maximum sloshing height of liquid. The results reveal that the nonlinearity is more significant in shallow tanks. Moreover, nonlinear hydrodynamic pressure distribution has no important difference with linear calculated pressure except for the surface sloshing pressure acting on the top of tanks. The linear ratio of depth of liquid to tank plan dimension used in ACI 350.3-06 formulation is found to be less accurate for calculating the maximum sloshing height of liquid.

Nonlinear dynamic response of seismically excited rectangular concrete liquid filled tanks

The effect of nonlinearity on behaviour of rectangular concrete tanks partially filled with water is studied. The nonlinearity in the numerical modeling of the surface liquid sloshing performance and hydrodynamic pressure initiates from unknown boundary conditions of contained liquid volume. The nonlinear simulations are performed for Time-History seismic analysis using the finite element software ABAQUS/CAE. The nonlinear results are compared with linear analytical solutions and ACI 350.3-06 code. A Paramedic study is conducted to investigate the effect of tank plan dimension, frequency content of different seismic ground motions, nature of earthquake movements, and interaction of bi-directional component of earthquake on the maximum sloshing height of liquid. The results reveal that the nonlinearity is more significant in shallow tanks. Moreover, nonlinear hydrodynamic pressure distribution has no important difference with linear calculated pressure except for the surface sloshing pressure acting on the top of tanks. The linear ratio of depth of liquid to tank plan dimension used in ACI 350.3-06 formulation is found to be less accurate for calculating the maximum sloshing height of liquid.

Contrast Analysis of Polarization in Three-Beam Interference Lithography

This paper analyzes the effect of polarization and the incident angle on the contrasts of interference patterns in three-beam interference lithography. A non-coplanar laser interference system was set up to simulate the relationship between contrast, beam polarization, and the incident angle. Different pattern periods require different incident angles, which means different contrast losses in interference lithography. Two different polarization modes were presented to study the effects of polarization with different incident angles based on theoretical analysis simulations. In the case of the co-directional component TE polarization mode, it was demonstrated that the pattern contrast decreases with the increase in the incident angle and the contrast loss caused by the polarization angle error also grew rapidly. By changing the mode to azimuthal (TE-TE-TE) polarization, the contrast of the interference pattern can be ensured to remain above 0.97 even though the incident angle is large. In addition, TE-TE-TE mode can accept larger polarization angle errors. This conclusion provides a theoretical basis for the generation of high-contrast light fields at different incident angles, and the conclusion is also applicable to multi-beam interference lithography.

Presenting Climate Projection Ensembles as Mean and Reasonable Worst Case, with Application to EURO-CORDEX Precipitation

Users of ensemble climate projections have choices with respect to how they interpret and apply the ensemble. A simplistic approach is to consider just the ensemble mean and ignore the individual ensemble members. A more thorough approach is to consider every ensemble member, although for complex impact models this may be unfeasible. Building on previous work in ensemble weather forecasting we explore an approach in-between these two extremes, in which the ensemble is represented by the mean and a reasonable worst case. The reasonable worst case is calculated using Directional Component Analysis (DCA), which is a simple statistical method that gives a robust estimate of worst-case for a given linear metric of impact, and which has various advantages relative to alternative definitions of worst-case. We present new mathematical results that clarify the interpretation of DCA and we illustrate DCA with an extensive set of synthetic examples. We then apply the mean and worst-case method based on DCA to EURO-CORDEX projections of future precipitation in Europe, with two different impact metrics. We conclude that the mean and worst-case method based on DCA is suitable for climate projection users who wish to explore the implications of the uncertainty around the ensemble mean without having to calculate the impacts of every ensemble member.

Radial and Directional Posteriors for Bayesian Deep Learning

We propose a new variational family for Bayesian neural networks. We decompose the variational posterior into two components, where the radial component captures the strength of each neuron in terms of its magnitude; while the directional component captures the statistical dependencies among the weight parameters. The dependencies learned via the directional density provide better modeling performance compared to the widely-used Gaussian mean-field-type variational family. In addition, the strength of input and output neurons learned via our posterior provides a structured way to compress neural networks. Indeed, experiments show that our variational family improves predictive performance and yields compressed networks simultaneously.

Influence of Active Part Stiffness on Radiated Sound Power Level in Power Transformers

Power transformers are associated with the radiation of unwanted noise in many circumstances due to its low frequency and relative high power, which reduction and mitigation is imperative. It is known that the main source of this noise are originated by the vibrations induced in the active part, namely the core, primarily due to electromagnetic forces and magnetomechanical effects. On the other hand, the laminated design of the core is indispensable in order to reduce the Foucault currents losses. Thus, in addition to the electrical requirements, the development of an appropriate model of the core dynamic behavior taking into account its segmented structure is urgent, in order to avoid resonances at any of the excitation frequencies. In the current proceeding, the influence of the core equivalent dynamic mechanical properties on a power transformer radiated noise was studied by performing a numerical parametric analysis. It was concluded that the active part stiffness properties, namely the directional component related to the out of lamination plane bending, ruled the vibroacoustic behavior of the transformer for the studied frequency range.