Uncertainty evaluation related with the fitting of probability distributions to rainfall experimental data

This work tackles the problem of finding a suitable statistical model to describe relevant glass properties, such as the strength under tensile stress. As known, glass is a brittle material, whose strength is strictly related to the presence of microcracks on its surface. The main issue is that the number of cracks, their size, and orientation are of random nature, and they may even change over time, due to abrasion phenomena. Consequently, glass strength should be statistically treated, but unfortunately none of the known probability distributions properly fit experimental data, when measured on abraded and/or aged glass panes. Owing to these issues, this paper proposes an innovative method to analyze the statistical properties of glass. The method takes advantage of the change of variable theorem and uses an ad-hoc transforming function to properly account for the distortion, on the original probability distribution of the glass strength, induced by the abrasion process. The adopted transforming function is based on micromechanical theory, and it provides an optimal fit of the experimental data.

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Probability Distributions of Peanut Seed Size

Peanut Science ◽

10.3146/i0095-3679-5-2-9 ◽

1978 ◽

Vol 5 (2) ◽

pp. 91-96 ◽

Cited By ~ 2

Author(s):

James I. Davidson ◽

Paul D. Blankenship ◽

Victor Chew

Keyword(s):

Experimental Data ◽

Seed Size ◽

Probability Distributions ◽

Logistic Distribution ◽

Agronomic Practices ◽

Harvest Dates ◽

Arachis Hypogaea L ◽

Mathematical Relationships ◽

Best Fit ◽

Standard Probability

Abstract Procedures and mathematical relationships were developed to describe seed size distributions for Florigiant, Florunner, and Starr peanut (Arachis hypogaea L.) varieties. Of six standard probability distributions studied, the normal and logistic distributions provided the best fit for the experimental data, These two distributions were therefore fitted to seed size data for several lots of peanuts. For each lot both the normal and logistic distributions provided an excellent fit to the experimental data, but the logistic was slightly superior. Differences between experimental and calculated values were greatest for lots that were the least or most mature. A logistic distribution was also fitted to the average of all data for each variety. These relationships may be used to better relate seed size to quality, marketing, shelling, and processing. They will also be useful in research studies of the effects on seed size of such variables as variety, agronomic practices, climate, soil moisture, and harvest dates.

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Experimental Investigation of the Nonlinear Effects on the Statistics of Vertical Motions and Loads of a Containership in Irregular Waves

Journal of Ship Research ◽

10.5957/jsr.2004.48.2.148 ◽

2004 ◽

Vol 48 (02) ◽

pp. 148-167 ◽

Cited By ~ 2

Author(s):

N. Fonseca ◽

C. Guedes Soares

Keyword(s):

Experimental Data ◽

Experimental Investigation ◽

Probability Distributions ◽

Nonlinear Behavior ◽

Nonlinear Effects ◽

Rayleigh Distribution ◽

Irregular Waves ◽

Cross Sectional ◽

Wave Heights ◽

Vertical Accelerations

The paper presents the results of an experimental investigation of the nonlinear effects on the vertical motions and loads on a containership model advancing in irregular waves. The experimental data are compared with numerical results from a nonlinear time domain strip method. The tests were carried out in a seakeeping tank using three sea states with significant wave heights of 4.2 m, 6.1 m, and 9.9 m, thus including very severe conditions. The measured responses include the absolute and relative motions, vertical accelerations, and cross-sectional loads at midship and ¼ Lpp from the forward perpendicular. The statistics of the experimental records demonstrate partly the nonlinear behavior of the responses, especially of the structural loads. The probability distributions of the positive and negative peaks show that the heave and pitch motions are only slightly asymmetric and their distributions compare well with the Rayleigh distribution. The vertical loads present distributions of peaks that are highly asymmetric and deviate from the Rayleigh distribution. Comparisons between simulated results and experimental data show that the numerical model is able to represent the nonlinear characteristics of the responses.

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Supporting Qualified Database for V&V and Uncertainty Evaluation of Best-Estimate System Codes

Volume 2B: Thermal Hydraulics ◽

10.1115/icone22-31273 ◽

2014 ◽

Cited By ~ 1

Author(s):

A. Petruzzi ◽

F. D’Auria

Keyword(s):

Experimental Data ◽

Reference Data ◽

Initial Conditions ◽

Heat Losses ◽

Uncertainty Evaluation ◽

Data Set ◽

Best Estimate ◽

Calculation Results ◽

Uncertainty Parameters

Uncertainty evaluation constitutes a key feature of BEPU (Best Estimate Plus Uncertainty) process. The uncertainty can be the result of a Monte Carlo type analysis involving input uncertainty parameters or the outcome of a process involving the use of experimental data and connected code calculations. Those uncertainty methods are discussed in several papers and guidelines (IAEA-SRS-52, OECD/NEA BEMUSE reports). The present paper aims at discussing the role and the depth of the analysis required for merging from one side suitable experimental data and on the other side qualified code calculation results. This aspect is mostly connected with the second approach for uncertainty mentioned above, but it can be used also in the framework of the first approach. Namely, the paper discusses the features and structure of the database that includes the following kinds of documents: 1. The” RDS-facility” (Reference Data Set for the selected facility): this includes the description of the facility, the geometrical characterization of any component of the facility, the instrumentations, the data acquisition system, the evaluation of pressure losses, the physical properties of the material and the characterization of pumps, valves and heat losses; 2. The “RDS-test” (Reference Data Set for the selected test of the facility): this includes the description of the main phenomena investigated during the test, the configuration of the facility for the selected test (possible new evaluation of pressure and heat losses if needed) and the specific boundary and initial conditions; 3. The “QP” (Qualification Report) of the code calculation results: this includes the description of the nodalization developed following a set of homogeneous techniques, the achievement of the steady state conditions and the qualitative and quantitative analysis of the transient with the characterization of the Relevant Thermal-Hydraulics Aspects (RTA); 4. The EH (Engineering Handbook) of the input nodalization: this includes the rationale adopted for each part of the nodalization, the user choices, and the systematic derivation and justification of any value present in the code input respect to the values as indicated in the RDS-facility and in the RDS-test.

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Contact Mechanics for Solids with Randomly Rough Surfaces and Plasticity

Lubricants ◽

10.3390/lubricants7100090 ◽

2019 ◽

Vol 7 (10) ◽

pp. 90 ◽

Cited By ~ 2

Author(s):

Avinash Tiwari ◽

Anle Wang ◽

Martin H. Müser ◽

B. N. J. Persson

Keyword(s):

Experimental Data ◽

Contact Mechanics ◽

Probability Distributions ◽

Power Spectra ◽

Short Length ◽

Length Scale ◽

Flat Surfaces ◽

Flow Processes ◽

Glass Surfaces ◽

Elastic And Plastic Deformation

We present experimental results for the elastic and plastic deformation of sandblasted polymer balls resulting from contacts with flat smooth steel and silica glass surfaces. Nearly symmetric, Gaussian-like height probability distributions were observed experimentally before and remarkably, also after the polymer balls were deformed plastically. For all the polymers studied we find that the surface roughness power spectra for large wavenumbers (short length scales) are nearly unchanged after squeezing the polymer balls against flat surfaces. We attribute this to non-uniform plastic flow processes at the micrometer length scale. The experimental data are analyzed using the Persson contact mechanics theory with plasticity and with finite-element method (FEM) calculations.

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Breakdown at Multiple Protrusions in SF6 and CO2

Energies ◽

10.3390/en13174449 ◽

2020 ◽

Vol 13 (17) ◽

pp. 4449

Author(s):

Odd Christian Feet ◽

Martin Seeger ◽

Daniel Over ◽

Kaveh Niayesh ◽

Frank Mauseth

Keyword(s):

Experimental Data ◽

Rough Surfaces ◽

Probability Distributions ◽

Gas Discharge ◽

Electric Breakdown ◽

Breakdown Field ◽

Weibull Distributions ◽

Electrode Area ◽

Breakdown Probability

The electric breakdown at single and multiple protrusions in SF6 and CO2 is investigated at 0.4 and 0.6 MPa, respectively. Additionally, the breakdown fields at rough surfaces of two different areas were determined. From the measurements, breakdown probability distributions for single protrusions were determined and fitted by Weibull distributions. This allowed the determination of statistical enlargement laws for the 50% breakdown probability fields E50. Such enlargement laws describe, for example, the scaling of breakdown field with electrode area or number of protrusions. The predictions were compared to the experimental data, and both agreement and discrepancies were observed depending on polarity and number of protrusions and gas. Discharge predictions including first electron, streamer inception and crossing, as well as leader propagation, gave further insight to this. It was found that predictions from enlargement laws based on statistical processes may not describe the measured breakdown fields well and that relevant physical breakdown criteria must also be considered.

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Application of Bayesian analysis to indirect Fourier transformation in small-angle scattering

Journal of Applied Crystallography ◽

10.1107/s0021889806035291 ◽

2006 ◽

Vol 39 (6) ◽

pp. 797-804 ◽

Cited By ~ 42

Author(s):

Bente Vestergaard ◽

Steen Hansen

Keyword(s):

Experimental Data ◽

Bayesian Analysis ◽

Small Angle ◽

Fourier Transformation ◽

Probability Distributions ◽

Small Angle Scattering ◽

Maximum Diameter ◽

Effective Number ◽

Extra Information ◽

Angle Scattering

Using Bayesian analysis for indirect Fourier transformation (IFT) of data from small-angle scattering (SAS) leads to probability distributions for parameters describing the experimental data. This quantification may provide extra information about the scattering system. The shape of the probability distribution for the maximum diameter of the scatterer may contain information aboute.g.the heterogeneity of the scattering sample. The information content in the experimental data can be quantified as an `effective number of parameters' which can be determined from the data. The applicability of the Bayesian approach to IFT in SAS is demonstrated using simulated as well as experimental data.

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