scholarly journals A Probabilistic Approach to Aeropropulsion System Assessment

2000 ◽  
Author(s):  
Michael T. Tong
Keyword(s):  
Mechanical Design ◽  
Probability Distributions ◽  
Probabilistic Approach ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Sensitivity Analyses ◽  
Turbine Engine ◽  
Technical Performance ◽  
Design Variables ◽  
System Assessment

A probabilistic approach is described for aeropropulsion system assessment. To demonstrate this approach, the technical performance of a wave rotor-enhanced gas turbine engine (i.e. engine net thrust, specific fuel consumption, and engine weight) is assessed. The assessment accounts for the uncertainties in component efficiencies/flows and mechanical design variables, using probability distributions. The results are presented in the form of cumulative distribution functions (CDFs) and sensitivity analyses, and are compared with those from the traditional deterministic approach. The comparison shows that the probabilistic approach provides a more realistic and systematic way to assess an aeropropulsion system.

Probabilistic finite element analysis in heat transfer to a nuclear fuel rod bumper support

2004 ◽  
Vol 218 (12) ◽  
pp. 1499-1505
Author(s):  
Rama Subba Reddy Gorla
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Nuclear Fuel ◽  
Cost Effective ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Element Analysis ◽  
Transfer Rates ◽  
Fuel Rod ◽  
Design Variables

Heat transfer from a nuclear fuel rod bumper support was computationally simulated by a finite element method and probabilistically evaluated in view of the several uncertainties in the performance parameters. Cumulative distribution functions and sensitivity factors were computed for overall heat transfer rates due to the thermodynamic random variables. These results can be used to identify quickly the most critical design variables in order to optimize the design and to make it cost effective. The analysis leads to the selection of the appropriate measurements to be used in heat transfer and to the identification of both the most critical measurements and the parameters.

scholarly journals Probabilistic Precipitation Forecast Postprocessing Using Quantile Mapping and Rank-Weighted Best-Member Dressing

2018 ◽  
Vol 146 (12) ◽  
pp. 4079-4098 ◽  
Author(s):  
Thomas M. Hamill ◽  
Michael Scheuerer
Keyword(s):  
Probability Distributions ◽  
The United States ◽  
Ensemble Forecast ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Precipitation Forecast ◽  
Prediction System ◽  
Quantile Mapping ◽  
State Dependent ◽  
Grid Points

Abstract Hamill et al. described a multimodel ensemble precipitation postprocessing algorithm that is used operationally by the U.S. National Weather Service (NWS). This article describes further changes that produce improved, reliable, and skillful probabilistic quantitative precipitation forecasts (PQPFs) for single or multimodel prediction systems. For multimodel systems, final probabilities are produced through the linear combination of PQPFs from the constituent models. The new methodology is applied to each prediction system. Prior to adjustment of the forecasts, parametric cumulative distribution functions (CDFs) of model and analyzed climatologies are generated using the previous 60 days’ forecasts and analyses and supplemental locations. The CDFs, which can be stored with minimal disk space, are then used for quantile mapping to correct state-dependent bias for each member. In this stage, the ensemble is also enlarged using a stencil of forecast values from the 5 × 5 surrounding grid points. Different weights and dressing distributions are assigned to the sorted, quantile-mapped members, with generally larger weights for outlying members and broader dressing distributions for members with heavier precipitation. Probability distributions are generated from the weighted sum of the dressing distributions. The NWS Global Ensemble Forecast System (GEFS), the Canadian Meteorological Centre (CMC) global ensemble, and the European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble forecast data are postprocessed for April–June 2016. Single prediction system postprocessed forecasts are generally reliable and skillful. Multimodel PQPFs are roughly as skillful as the ECMWF system alone. Postprocessed guidance was generally more skillful than guidance using the Gamma distribution approach of Scheuerer and Hamill, with coefficients generated from data pooled across the United States.

Probabilistic Framework for Uncertainty Propagation With Both Probabilistic and Interval Variables

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Kais Zaman ◽  
Mark McDonald ◽  
Sankaran Mahadevan
Keyword(s):  
System Analysis ◽  
Epistemic Uncertainty ◽  
Probability Distributions ◽  
Uncertainty Propagation ◽  
Probabilistic Approach ◽  
Interval Data ◽  
Cumulative Distribution ◽  
System Response ◽  
Computationally Efficient ◽  
Probabilistic Uncertainty

This paper develops and illustrates a probabilistic approach for uncertainty representation and propagation in system analysis, when the information on the uncertain input variables and/or their distribution parameters may be available as either probability distributions or simply intervals (single or multiple). A unique aggregation technique is used to combine multiple interval data and to compute rigorous bounds on the system response cumulative distribution function. The uncertainty described by interval data is represented through a flexible family of probability distributions. Conversion of interval data to a probabilistic format enables the use of computationally efficient methods for probabilistic uncertainty propagation. Two methods are explored for the implementation of the proposed approach, based on (1) sampling and (2) optimization. The sampling-based strategy is more expensive and tends to underestimate the output bounds. The optimization-based methodology improves both aspects. The proposed methods are used to develop new solutions to challenge problems posed by the Sandia epistemic uncertainty workshop (Oberkampf et al., 2004, “Challenge Problems: Uncertainty in System Response Given Uncertain Parameters,” Reliab. Eng. Syst. Saf., 85, pp. 11–19). Results for the challenge problems are compared with earlier solutions.

scholarly journals THE IMPACT OF SPATIAL AND TEMPORAL RESOLUTIONS IN TROPICAL SUMMER RAINFALL DISTRIBUTION: PRELIMINARY RESULTS

2017 ◽  
Vol IV-4/W2 ◽  
pp. 183-191
Author(s):  
Q. Liu ◽  
L. S Chiu ◽  
X. Hao
Keyword(s):  
Climate Models ◽  
Hydrological Cycle ◽  
Probability Distributions ◽  
Summer Rainfall ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Statistical Parameters ◽  
Spatial And Temporal Scales ◽  
Gamma Distributions ◽  
The Impact

The abundance or lack of rainfall affects peoples’ life and activities. As a major component of the global hydrological cycle (Chokngamwong & Chiu, 2007), accurate representations at various spatial and temporal scales are crucial for a lot of decision making processes. Climate models show a warmer and wetter climate due to increases of Greenhouse Gases (GHG). However, the models’ resolutions are often too coarse to be directly applicable to local scales that are useful for mitigation purposes. Hence disaggregation (downscaling) procedures are needed to transfer the coarse scale products to higher spatial and temporal resolutions. The aim of this paper is to examine the changes in the statistical parameters of rainfall at various spatial and temporal resolutions. The TRMM Multi-satellite Precipitation Analysis (TMPA) at 0.25 degree, 3 hourly grid rainfall data for a summer is aggregated to 0.5,1.0, 2.0 and 2.5 degree and at 6, 12, 24 hourly, pentad (five days) and monthly resolutions. The probability distributions (PDF) and cumulative distribution functions(CDF) of rain amount at these resolutions are computed and modeled as a mixed distribution. Parameters of the PDFs are compared using the Kolmogrov-Smironov (KS) test, both for the mixed and the marginal distribution. These distributions are shown to be distinct. The marginal distributions are fitted with Lognormal and Gamma distributions and it is found that the Gamma distributions fit much better than the Lognormal.

Discrete Pareto Distributions

2014 ◽  
Vol 29 (2) ◽  
Author(s):  
Amrutha Buddana ◽  
Tomasz J. Kozubowski
Keyword(s):  
Probability Distributions ◽  
Probability Generating Function ◽  
Tail Probability ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Random Sums ◽  
Pareto Distributions ◽  
Discretization Schemes ◽  
Stochastic Representations ◽  
Divisibility Properties

AbstractWe review several common discretization schemes and study a particular class of power-tail probability distributions on integers, obtained by discretizing continuous Pareto II (Lomax) distribution through one of them. Our results include expressions for the density and cumulative distribution functions, probability generating function, moments and related parameters, stability and divisibility properties, stochastic representations, and limiting distributions of random sums with discrete-Pareto number of terms. We also briefly discuss issues of simulation and estimation and extensions to multivariate setting.

scholarly journals Valuation of Exchange Option with Credit Risk in a Hybrid Model

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2091
Author(s):  
Geonwoo Kim
Keyword(s):  
Credit Risk ◽  
Hybrid Model ◽  
Structural Model ◽  
Risk Model ◽  
Probabilistic Approach ◽  
Option Price ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Reduced Form ◽  
Exchange Option

In this paper, the valuation of the exchange option with credit risk under a hybrid credit risk model is investigated. In order to build the hybrid model, we consider both the reduced-form model and the structural model. We adopt the probabilistic approach to derive the closed-form formula of an exchange option price with credit risk under the proposed model. Specifically, the change of measure technique is used repeatedly, and the pricing formula is provided as the standard normal cumulative distribution functions.

The joint probability distribution function of structure factors with rational indices. IV. The P1 case

1999 ◽  
Vol 55 (3) ◽  
pp. 512-524
Author(s):  
Carmelo Giacovazzo ◽  
Dritan Siliqi ◽  
Cristina Fernández-Castaño
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Probabilistic Approach ◽  
Joint Probability ◽  
Distribution Functions ◽  
Accurate Estimation ◽  
Joint Probability Distribution ◽  
Structure Factors ◽  
Joint Probability Distributions ◽  
The Hilbert Transform

The method of the joint probability distribution functions of structure factors has been extended to reflections with rational indices. The most general case, space group P1, has been considered. The positional parameters are the primitive random variables of our probabilistic approach, while the reflection indices are kept fixed. Quite general joint probability distributions have been considered from which conditional distributions have been derived: these proved applicable to the accurate estimation of the real and imaginary parts of a structure factor, given prior information on other structure factors. The method is also discussed in relation to the Hilbert-transform techniques.

Unsteady Fluid Structure Interaction in a Turbine Blade

2005 ◽  
Author(s):  
Rama Subba Reddy Gorla ◽  
Shantaram S. Pai ◽  
Isaiah Blankson ◽  
Srinivas C. Tadepalli ◽  
Sreekantha Reddy Gorla
Keyword(s):  
Finite Element ◽  
Turbine Blade ◽  
Three Dimensional ◽  
Cost Effective ◽  
Computer Time ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Navier Stokes ◽  
Rotating Frame ◽  
Design Variables

An unsteady, three dimensional Navier-Stokes solution in rotating frame formulation for turbomachinery applications has been described. Casting the governing equations in a rotating frame enables the freezing of grid motion and results in substantial savings in computer time. Heat transfer to a gas turbine blade was computationally simulated by finite element methods and probabilistically evaluated in view of the several uncertainties in the performance parameters. The interconnection between the CFD code and finite element structural analysis code was necessary to couple the thermal profiles with the structural design. The stresses and their variations were evaluated at critical points on the turbine blade. Cumulative distribution functions and sensitivity factors were computed for stresses due to the aerodynamic, geometric, material and thermal random variables. These results can be used to quickly identify the most critical design variables in order to optimize the design and make it cost effective. The analysis leads to the selection of the appropriate materials to be used and to the identification of both the most critical measurements and parameters.

scholarly journals Probabilistic Study of Fluid Structure Interaction

2002 ◽  
Author(s):  
Rama S. R. Gorla ◽  
Shantaram S. Pai ◽  
Jeffrey J. Rusick
Keyword(s):  
Stress Responses ◽  
Hoop Stress ◽  
Coefficient Of Thermal Expansion ◽  
Cost Effective ◽  
Distribution Functions ◽  
Flow Coefficient ◽  
Cumulative Distribution ◽  
Design Variables ◽  
Probabilistic Study ◽  
Combustor Liner

A combustor liner was computationally simulated and probabilistically evaluated in view of the several uncertainties in the aerodynamic, structural, material and thermal variables that govern the combustor liner. The interconnection between the computational fluid dynamics code and the finite element structural analysis codes was necessary to couple the thermal profiles with structural design. The stresses and their variations were evaluated at critical points on the liner. Cumulative distribution functions and sensitivity factors were computed for stress responses due to the aerodynamic, mechanical and thermal random variables. It was observed that the inlet and exit temperatures have a lot of influence on the hoop stress. For prescribed values of inlet and exit temperatures, the Reynolds number of the flow, coefficient of thermal expansion, gas emissivity and absorptivity and thermal conductivity of the material have about the same impact on the hoop stress. These results can be used to quickly identify the most critical design variables in order to optimize the design and make it cost effective.

scholarly journals Statistical theory of probabilistic hazard maps: a probability distribution for the hazard boundary location

2018 ◽  
Author(s):  
David M. Hyman ◽  
Andrea Bevilacqua ◽  
Marcus I. Bursik
Keyword(s):  
Standard Deviation ◽  
Mass Flow ◽  
Probability Distributions ◽  
Analytic Solutions ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Hazard Maps ◽  
Statistical Measures ◽  
Boundary Location ◽  
The Mean

Abstract. The study of volcanic mass flow hazards in a probabilistic framework centers around systematic experimental numerical modelling of the hazardous phenomenon and the subsequent generation and interpretation of a probabilistic hazard map (PHM). For a given volcanic flow (e.g., lava flow, lahar, pyroclastic flow, etc.), the PHM is typically interpreted as the point-wise probability of flow material inundation. In the current work, we present new methods for calculating spatial representations of the mean, standard deviation, median, and modal locations of the hazard's boundary as ensembles of many deterministic runs of a physical model. By formalizing its generation and properties, we show that a PHM may be used to construct these statistical measures of the hazard boundary which have been unrecognized in previous probabilistic hazard analyses. Our formalism shows that a typical PHM for a volcanic mass flow not only gives the point-wise inundation probability, but also represents a set of cumulative distribution functions for the location of the inundation boundary with a corresponding set of probability density functions. These distributions run over curves of steepest ascent on the PHM. Consequently, 2D space curves can be constructed on the map which represent the mean, median and modal locations of the likely inundation boundary. These curves give well-defined answers to the question of the likely boundary location of the area impacted by the hazard. Additionally, methods of calculation for higher moments including the standard deviation are presented which take the form of map regions surrounding the mean boundary location. These measures of central tendency and variance add significant value to spatial probabilistic hazard analyses, giving a new statistical description of the probability distributions underlying PHMs. The theory presented here may be used to construct improved hazard maps, which could prove useful for planning and emergency management purposes. This formalism also allows for application to simplified processes describable by analytic solutions. In that context, the connection between the PHM, its moments, and the underlying parameter variation is explicit, allowing for better source parameter estimation from natural data, yielding insights about natural controls on those parameters.

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