Appendix II: Additional Technique for Distribution Shape Not Assumed

2009 ◽  
pp. 68-68-1
Keyword(s):  
Distribution Shape

STRUCTURAL RELIABILITY ANALYSIS BASED ON P-BOXES

2020 ◽  
Vol 92 (6) ◽  
pp. 51-58
Author(s):  
S.A. SOLOVYEV ◽  
Keyword(s):  
Probability Distribution ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Epistemic Uncertainty ◽  
Random Variable ◽  
Strength Criterion ◽  
Structural Elements ◽  
Structural Element ◽  
Limit States ◽  
Distribution Shape

The article describes a method for reliability (probability of non-failure) analysis of structural elements based on p-boxes. An algorithm for constructing two p-blocks is shown. First p-box is used in the absence of information about the probability distribution shape of a random variable. Second p-box is used for a certain probability distribution function but with inaccurate (interval) function parameters. The algorithm for reliability analysis is presented on a numerical example of the reliability analysis for a flexural wooden beam by wood strength criterion. The result of the reliability analysis is an interval of the non-failure probability boundaries. Recommendations are given for narrowing the reliability boundaries which can reduce epistemic uncertainty. On the basis of the proposed approach, particular methods for reliability analysis for any structural elements can be developed. Design equations are given for a comprehensive assessment of the structural element reliability as a system taking into account all the criteria of limit states.

W-Peakedness: A Simulation based Study

2015 ◽  
Vol 1 (1) ◽  
Author(s):  
Suboohi Safdar ◽  
Dr. Ejaz Ahmed
Keyword(s):  
Probability Distributions ◽  
Extensive Study ◽  
Descriptive Statistics ◽  
Target Point ◽  
Density Functions ◽  
Central Value ◽  
Distribution Shape ◽  
Simulation Based ◽  
Different Shapes ◽  
Kurtosis Coefficient

Kurtosis is a commonly used descriptive statistics. Kurtosis “Coefficient of excess” is critically reviewed in different aspects and is called as, measuring the fatness of the tails of the density functions, concentration towards the central value, scattering away from the target point or degree of peakedness of probability distribution. Kurtosis is referred to the shape of the distribution but many distributions having same kurtosis value may have different shapes while Kurtosis may exist when peak of a distribution is not in existence. Through extensive study of kurtosis on several distributions, Wu (2002) introduced a new measure called “W-Peakedness” that offers a fine capture of distribution shape to provide an intuitive measure of peakedness of the distribution which is inversely proportional to the standard deviation of the distribution. In this paper the work is extended for different others continuous probability distributions. Empirical results through simulation illustrate the proposed method to evaluate kurtosis by W-peakedness

scholarly journals EFFECTS OF POROSITY ON ULTRASONIC CHARACTERISTIC PARAMETERS AND MECHANICAL PROPERTIES OF GLASS FIBER REINFORCED COMPOSITES

2012 ◽  
Vol 06 ◽  
pp. 646-651 ◽  
Author(s):  
Wen Ma ◽  
Fushun Liu
Keyword(s):  
Mechanical Properties ◽  
Ultrasonic Attenuation ◽  
Ultrasonic Inspection ◽  
Fiber Reinforced Composites ◽  
Metallographic Analysis ◽  
Void Content ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Characteristic Parameters ◽  
Distribution Shape

Voids are inevitable in the fabrication of fiber reinforced composites and have a detrimental impact on mechanical properties of composites. Different void contents were acquired by applying different vacuum bag pressures. Ultrasonic inspection and ablation density method were adopted to measure the ultrasonic characteristic parameters and average porosity, the characterization of voids' distribution, shape and size were carried out through metallographic analysis. Effects of void content on the tensile, flexural and interlaminar shear properties and the ultrasonic characteristic parameters were discussed. The results showed that, as vacuum bag pressure went from -50kPa to -98kPa, the voids content decreased from 4.36 to 0.34, the ultrasonic attenuation coefficient decreased, but the mechanical strengths all increased.

Image based portable wear debris analysis tool

2015 ◽  
Vol 67 (4) ◽  
pp. 389-398 ◽  
Author(s):  
Muhammad Ali Khan ◽  
Ahmed Farooq Cheema ◽  
Sohaib Zia Khan ◽  
Shafiq-ur-Rehman Qureshi
Keyword(s):  
Real Time ◽  
Wear Debris ◽  
Machine Component ◽  
Analysis Tool ◽  
Content Type ◽  
Real Time Analysis ◽  
Distribution Shape ◽  
Basic Features ◽  
Health Diagnosis ◽  
Wear Debris Analysis

Purpose – The purpose of this paper is to show the development of an image processing-based portable equipment for an automatic wear debris analysis. It can analyze both the qualitative and quantitative features of machine wear debris: size, quantity, size distribution, shape, surface texture and material composition via color. Design/methodology/approach – It comprises hardware and software components which can take debris in near real-time from a machine oil sump and process it for features diagnosis. This processing provides the information of the basic features on the user screen which can further be used for machine component health diagnosis. Findings – The developed system has the capacity to replace the existing off-line methods due to its cost effectiveness and simplicity in operation. The system is able to analyze debris basic quantitative and qualitative features greater than 50 micron and less than 300 micron. Originality/value – Wear debris basic features analysis tool is developed and discussed. The portable and near real-time analysis offered by the discussed work can be more technically effective as compared to the existing off-line and online techniques.

scholarly journals A Robust Dual-Frequency Radar Profiling Algorithm

2011 ◽  
Vol 50 (7) ◽  
pp. 1543-1557 ◽  
Author(s):  
Mircea Grecu ◽  
Lin Tian ◽  
William S. Olson ◽  
Simone Tanelli
Keyword(s):  
Synthetic Data ◽  
Optimization Procedure ◽  
Correction Method ◽  
Single Frequency ◽  
Retrieval Algorithm ◽  
Dual Frequency ◽  
Ka Band ◽  
Radar Observations ◽  
Distribution Shape ◽  
Ku Band

AbstractIn this study, an algorithm to retrieve precipitation from spaceborne dual-frequency (13.8 and 35.6 GHz, or Ku/Ka band) radar observations is formulated and investigated. Such algorithms will be of paramount importance in deriving radar-based and combined radar–radiometer precipitation estimates from observations provided by the forthcoming NASA Global Precipitation Measurement (GPM) mission. In GPM, dual-frequency Ku-/Ka-band radar observations will be available only within a narrow swath (approximately one-half of the width of the Ku-band radar swath) over the earth’s surface. Therefore, a particular challenge is to develop a flexible radar retrieval algorithm that can be used to derive physically consistent precipitation profile estimates across the radar swath irrespective of the availability of Ka-band radar observations at any specific location inside that swath, in other words, an algorithm capable of exploiting the information provided by dual-frequency measurements but robust in the absence of Ka-band channel. In the present study, a unified, robust precipitation retrieval algorithm able to interpret either Ku-only or dual-frequency Ku-/Ka-band radar observations in a manner consistent with the information content of the observations is formulated. The formulation is based on 1) a generalized Hitschfeld–Bordan attenuation correction method that yields generic Ku-only precipitation profile estimates and 2) an optimization procedure that adjusts the Ku-band estimates to be physically consistent with coincident Ka-band reflectivity observations and surface reference technique–based path-integrated attenuation estimates at both Ku and Ka bands. The algorithm is investigated using synthetic and actual airborne radar observations collected in the NASA Tropical Composition, Cloud, and Climate Coupling (TC4) campaign. In the synthetic data investigation, the dual-frequency algorithm performed significantly better than a single-frequency algorithm; dual-frequency estimates, however, are still sensitive to various assumptions such as the particle size distribution shape, vertical and cloud water distributions, and scattering properties of the ice-phase precipitation.

scholarly journals Statistical Downscaling of Daily Wind Speed Variations

2014 ◽  
Vol 53 (3) ◽  
pp. 660-675 ◽  
Author(s):  
Megan C. Kirchmeier ◽  
David J. Lorenz ◽  
Daniel J. Vimont
Keyword(s):  
Wind Speed ◽  
Gamma Distribution ◽  
Large Scale ◽  
Probabilistic Method ◽  
Probabilistic Approach ◽  
Local Scale ◽  
Scale Parameters ◽  
Wind Speeds ◽  
Distribution Shape ◽  
Realistic Information

AbstractThis study presents the development of a method to statistically downscale daily wind speed variations in an extended Great Lakes region. A probabilistic approach is used, predicting a daily-varying probability density function (PDF) of local-scale daily wind speed conditioned on large-scale daily wind speed predictors. Advantages of a probabilistic method are that it provides realistic information on the variance and extremes in addition to information on the mean, it allows the autocorrelation of downscaled realizations to be tuned to match the autocorrelation of local-scale observations, and it allows flexibility in the use of the final downscaled product. Much attention is given to fitting the proper functional form of the PDF by investigating the observed local-scale wind speed distribution (predictand) as a function of the decile of the large-scale wind (predictor). It is found that the local-scale standard deviation and the local-scale shape parameter (from a gamma distribution) are nonconstant functions of the large-scale predictor. As such, a vector generalized linear model is developed to relate the large-scale and local-scale wind speeds. Maximum likelihood and cross validation are used to fit local-scale gamma distribution shape and scale parameters to the large-scale wind speed. The result is a daily-varying probability distribution of local-scale wind speed, conditioned on the large-scale wind speed.

Detection of Compositional Fluctuations in High Temperature Exposed Waspaloy

2001 ◽  
Vol 699 ◽  
Author(s):  
Xiaodong Zou ◽  
Tariq Makram ◽  
Rosario A. Gerhardt
Keyword(s):  
Exposure Time ◽  
Structural Integrity ◽  
Thermal Exposure ◽  
X Ray Diffraction ◽  
X Ray ◽  
Gamma Prime ◽  
Distribution Shape ◽  
The Matrix ◽  
Quantitative Stereology ◽  
Nickel Base

AbstractWaspaloy is a nickel base super-alloy used in aircraft engines. When this alloy is placed in service, it is subjected to long term exposure at high temperatures, which can cause the reinforcing gamma prime precipitate population to fluctuate and thus affect its structural integrity. The population fluctuates as a result of coarsening, dissolution or re-precipitation. Samples exposed to 1200° F for times ranging from 0 to 12626 hours were characterized using impedance spectroscopy, microhardness measurements, x-ray diffraction and quantitative stereology. Two important parameters were derived from the impedance measurements: (1) the imaginary admittance peak magnitude (Ymax) and (2) the associated relaxation frequency (fmax). As the distribution, shape and size of the precipitates change with exposure time, these parameters were also found to vary. In addition to the changes in precipitate geometry, lattice constant changes detected by analyzing x-ray diffraction data suggest that there are compositional shifts in the matrix as well as the gamma prime precipitates. Furthermore, the preferred orientation of the precipitates can also be seen to change with exposure time. These changes in composition, size and shape as a function of thermal exposure time are accompanied by changes in the volume fractions of primary and secondary gamma prime particles present. Using effective medium models, it is possible to predict that the measured properties are related to the gamma prime population. The grain boundary carbides do not appear to play any role at the conditions presented.

The Behavior of Number Concentration Tendencies for the Continuous Collection Growth Equation Using One- and Two-Moment Bulk Parameterization Schemes

2007 ◽  
Vol 46 (8) ◽  
pp. 1264-1274
Author(s):  
Jerry M. Straka ◽  
Katharine M. Kanak ◽  
Matthew S. Gilmore
Keyword(s):  
Growth Process ◽  
Number Concentration ◽  
Mathematical Explanation ◽  
Growth Equation ◽  
Parameterization Schemes ◽  
Distribution Shape ◽  
Bulk Parameterization

Abstract This paper presents a mathematical explanation for the nonconservation of total number concentration Nt of hydrometeors for the continuous collection growth process, for which Nt physically should be conserved for selected one- and two-moment bulk parameterization schemes. Where possible, physical explanations are proposed. The assumption of a constant no in scheme A is physically inconsistent with the continuous collection growth process, as is the assumption of a constant Dn for scheme B. Scheme E also is nonconservative, but it seems this result is not because of a physically inconsistent specification; rather the solution scheme’s equations simply do not satisfy Nt conservation and Nt does not come into the derivation. Even scheme F, which perfectly conserves Nt, does not preserve the distribution shape in comparison with a bin model.

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