4,460 research outputs found
Importance sampling the union of rare events with an application to power systems analysis
We consider importance sampling to estimate the probability of a union
of rare events defined by a random variable . The
sampler we study has been used in spatial statistics, genomics and
combinatorics going back at least to Karp and Luby (1983). It works by sampling
one event at random, then sampling conditionally on that event
happening and it constructs an unbiased estimate of by multiplying an
inverse moment of the number of occuring events by the union bound. We prove
some variance bounds for this sampler. For a sample size of , it has a
variance no larger than where is the union
bound. It also has a coefficient of variation no larger than
regardless of the overlap pattern among the
events. Our motivating problem comes from power system reliability, where the
phase differences between connected nodes have a joint Gaussian distribution
and the rare events arise from unacceptably large phase differences. In the
grid reliability problems even some events defined by constraints in
dimensions, with probability below , are estimated with a
coefficient of variation of about with only sample
values
Evaluating the Differences of Gridding Techniques for Digital Elevation Models Generation and Their Influence on the Modeling of Stony Debris Flows Routing: A Case Study From Rovina di Cancia Basin (North-Eastern Italian Alps)
Debris \ufb02ows are among the most hazardous phenomena in mountain areas. To cope
with debris \ufb02ow hazard, it is common to delineate the risk-prone areas through
routing models. The most important input to debris \ufb02ow routing models are the
topographic data, usually in the form of Digital Elevation Models (DEMs). The quality
of DEMs depends on the accuracy, density, and spatial distribution of the sampled
points; on the characteristics of the surface; and on the applied gridding methodology.
Therefore, the choice of the interpolation method affects the realistic representation
of the channel and fan morphology, and thus potentially the debris \ufb02ow routing
modeling outcomes. In this paper, we initially investigate the performance of common
interpolation methods (i.e., linear triangulation, natural neighbor, nearest neighbor,
Inverse Distance to a Power, ANUDEM, Radial Basis Functions, and ordinary kriging)
in building DEMs with the complex topography of a debris \ufb02ow channel located
in the Venetian Dolomites (North-eastern Italian Alps), by using small footprint full-
waveform Light Detection And Ranging (LiDAR) data. The investigation is carried
out through a combination of statistical analysis of vertical accuracy, algorithm
robustness, and spatial clustering of vertical errors, and multi-criteria shape reliability
assessment. After that, we examine the in\ufb02uence of the tested interpolation algorithms
on the performance of a Geographic Information System (GIS)-based cell model for
simulating stony debris \ufb02ows routing. In detail, we investigate both the correlation
between the DEMs heights uncertainty resulting from the gridding procedure and
that on the corresponding simulated erosion/deposition depths, both the effect of
interpolation algorithms on simulated areas, erosion and deposition volumes, solid-liquid
discharges, and channel morphology after the event. The comparison among the tested
interpolation methods highlights that the ANUDEM and ordinary kriging algorithms
are not suitable for building DEMs with complex topography. Conversely, the linear
triangulation, the natural neighbor algorithm, and the thin-plate spline plus tension and completely regularized spline functions ensure the best trade-off among accuracy
and shape reliability. Anyway, the evaluation of the effects of gridding techniques on
debris \ufb02ow routing modeling reveals that the choice of the interpolation algorithm does
not signi\ufb01cantly affect the model outcomes
Digital image correlation (DIC) analysis of the 3 December 2013 Montescaglioso landslide (Basilicata, Southern Italy). Results from a multi-dataset investigation
Image correlation remote sensing monitoring techniques are becoming key tools for
providing effective qualitative and quantitative information suitable for natural hazard assessments,
specifically for landslide investigation and monitoring. In recent years, these techniques have
been successfully integrated and shown to be complementary and competitive with more standard
remote sensing techniques, such as satellite or terrestrial Synthetic Aperture Radar interferometry.
The objective of this article is to apply the proposed in-depth calibration and validation analysis,
referred to as the Digital Image Correlation technique, to measure landslide displacement.
The availability of a multi-dataset for the 3 December 2013 Montescaglioso landslide, characterized
by different types of imagery, such as LANDSAT 8 OLI (Operational Land Imager) and TIRS
(Thermal Infrared Sensor), high-resolution airborne optical orthophotos, Digital Terrain Models
and COSMO-SkyMed Synthetic Aperture Radar, allows for the retrieval of the actual landslide
displacement field at values ranging from a few meters (2–3 m in the north-eastern sector of the
landslide) to 20–21 m (local peaks on the central body of the landslide). Furthermore, comprehensive
sensitivity analyses and statistics-based processing approaches are used to identify the role of the
background noise that affects the whole dataset. This noise has a directly proportional relationship to
the different geometric and temporal resolutions of the processed imagery. Moreover, the accuracy
of the environmental-instrumental background noise evaluation allowed the actual displacement
measurements to be correctly calibrated and validated, thereby leading to a better definition of
the threshold values of the maximum Digital Image Correlation sub-pixel accuracy and reliability
(ranging from 1/10 to 8/10 pixel) for each processed dataset
Primary Dendrite Distribution and Disorder During Directional Solidification of Pb-Sb Alloys
Pb-2.2 wt pct Sb and Pb-5.8 wt pet Sb alloys have been directionally solidified from a single-crystal seed with its [100] orientation parallel to the growth direction, to examine the primary dendrite distribution and disorder of the dendrite arrays. The dendrite distribution and ordering have been investigated using analysis techniques such as the Gauss-amplitude fit to the frequency distribution of nearest and higher-order spacings, minimum spanning tree (MST), Voronoi polygon, and Fourier transform (FT) of the dendrite centers. Since the arrangement of dendrites is driven by the requirement to accommodate side-branch growth along the (100) directions, the FT images of the fully developed dendrite centers contain spots which indicate this preferred alignment. A directional solidification distance of about three mushy-zone lengths is sufficient to ensure a steady-state dendritic array, in terms of reaching a constant mean primary spacing. However, local dendrite ordering continues throughout the directional solidification process. The interdendritic convection not only decreases the mean primary spacing, it also makes the dendrite array more disordered and reduces the ratio of the upper and lower spacing limits, as defined by the largest 5 pct and the smallest 5 pct of the population
Cellular Array Morphology During Directional Solidification
Cellular array morphology has been examined in the shallow cell, deep cell, and cell-to-dendrite transition regime in Pb-2.2 wt pct Sb and Al-4.1 wt pct Cu alloy single-crystal samples that were directionally solidified along [100]. Statistical analysis of the cellular spacing distribution on transverse sections has been carried out using minimum spanning tree (MST), Voronoi polygons, radial distribution factor, and fast Fourier transform (FFT) techniques. The frequency distribution of the number of nearest neighbors and the MST parameters suggest that the arrangement of cells may be visualized as a hexagonal tessellation with superimposed 50 pct random noise. However, the power spectrum of the Fourier transform of the cell centers shows a diffused single-ring pattern that does not agree with the power spectrum from the hexagonal tessellation having a 50 pct superimposed random (uniformly distributed or Gaussian) noise. The radial distribution factor obtained from the cells is similar to that of liquids. An overall steady-state distribution in terms of the mean primary spacing is achieved after directional solidification of about three mushy-zone lengths. However, the process of nearest-neighbor interaction continues throughout directional solidification, as indicated by about 14 pct of the cells undergoing submerging in the shallow cell regime or by an increasing first and second nearest-neighbor ordering along the growth direction for the cells at the cell-to-dendrite transition. The nature of cell distribution in the Al-Cu alloy appears to be the same as that in the Pb-Sb. The ratio between the upper and lower limits of the primary spacing, as defined by the largest and the smallest 10 pct of the population, respectively, is constant: 1.43 +/- 0.11. It does not depend upon the solidification processing conditions
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