Best-Estimate Plus Uncertainty Analysis of CANDU Fuel Reliability Using Manufacturing and Simulated Core Data

2020 ◽  
Vol 6 (4) ◽  
Author(s):  
Jason J. Song ◽  
Paul K. Chan ◽  
Hugues W. Bonin ◽  
Mahesh Pandey
Keyword(s):  
Internal Pressure ◽  
Probability Distributions ◽  
Real Data ◽  
Simulation Method ◽  
Failure Criteria ◽  
Hoop Strain ◽  
Fuel Performance ◽  
Best Estimate ◽  
Average Improvement ◽  
Centerline Temperature

Abstract A novel method of assessing the reliability of 37-element Canada deuterium uranium (reactor) (CANDU) fuel bundle was explored. The method implements a “best-estimate plus uncertainty” (BEPU) approach where a probabilistic treatment of manufacturing and operating inputs is used to predict fuel performance. The fuel performance was predicted using the Canadian industry standard codes for fuel performance, ELESTRESS and ELOCA, which, respectively, model fuel behaviors during normal and transient conditions. The outputs of the codes were compared against failure criteria from industry norms to determine the probability of failure. A Monte Carlo simulation method was applied to analyze this problem. Probability distributions of manufacturing input variables were estimated from real data, which were then randomly sampled. The inputs for fuel burnup and power were simulated using core-following data generated using a three-dimensional diffusion code, the Reactor Fuelling Simulation Program (RFSP), which were also then randomly sampled. The results of the simulations predict significant improvements in margins to limits for all performance parameters. An average improvement of 500 °C in centerline temperature, 10 °C in sheath temperature, 12 MPa in element internal pressure, and 0.8% in pellet end sheath hoop strain was predicted for the highest-powered region of the core, during normal operations, in comparison with the limit-of-envelope (LOE) benchmark. An 80% reactor overhead break (ROH) transient simulation was also simulated, and an average improvement of 500 °C in centerline temperature, 150 °C in sheath temperature, 6.5 MPa in internal pressure, and 2% in sheath hoop strain was predicted.

scholarly journals Moment based Estimation for the Shape Parameters, Effect it on Some Probability Statistical Distributions Using the Moment Method and Maximum Likelihood Method

2020 ◽  
Vol 5 (6) ◽  
pp. 979-986
Author(s):  
Hassan Tawakol A. Fadol
Keyword(s):  
Maximum Likelihood ◽  
Shape Parameter ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Estimation Method ◽  
Simulation Method ◽  
Likelihood Method ◽  
Inductive Method ◽  
Binomial Distributions ◽  
Best Estimate

The purpose of this paper was to identify the values of the parameters of the shape of the binomial, bias one and natural distributions. Using the estimation method and maximum likelihood Method, the criterion of differentiation was used to estimate the shape parameter between the probability distributions and to arrive at the best estimate of the parameter of the shape when the sample sizes are small, medium, The problem was to find the best estimate of the characteristics of the society to be estimated so that they are close to the estimated average of the mean error squares and also the effect of the estimation method on estimating the shape parameter of the distributions at the sizes of different samples In the values of the different shape parameter, the descriptive and inductive method was selected in the analysis of the data by generating 1000 random numbers of different sizes using the simulation method through the MATLAB program. A number of results were reached, 10) to estimate the small shape parameter (0.3) for binomial distributions and Poisson and natural and they can use the Poisson distribution because it is the best among the distributions, and to estimate the parameter of figure (0.5), (0.7), (0.9) Because it is better for binomial binomial distributions, when the size of a sample (70) for a teacher estimate The small figure (0.3) of the binomial and boson distributions and natural distributions can be used for normal distribution because it is the best among the distributions.

scholarly journals Multiphysics Modeling of Thorium-Based Fuel Performance With Cr-Coated SiC/SiC Composite Under Normal and Accident Conditions

2021 ◽  
Vol 9 ◽  
Author(s):  
Shengyu Liu ◽  
Rong Liu ◽  
Chengjie Qiu ◽  
Wenzhong Zhou
Keyword(s):  
Failure Time ◽  
Mechanical Performance ◽  
Hoop Strain ◽  
Fuel Performance ◽  
Multiphysics Modeling ◽  
Normal Operating ◽  
Loss Of Coolant Accident ◽  
Accident Conditions ◽  
Work First ◽  
Centerline Temperature

Using the finite element multiphysics modeling method, the performance of the thorium-based fuel with Cr-coated SiC/SiC composite cladding under both normal operating and accident conditions was investigated in this work. First, the material properties of SiC/SiC composite and chromium were reviewed. Then, the implemented model was simulated, and the results were compared with those of the FRAPTRAN code to verify the correctness of the model used in this work. Finally, the fuel performance of the Th0.923U0.077O2 fuel, Th0.923Pu0.077O2 fuel, and UO2 fuel combined with the Cr-coated SiC/SiC composite cladding and Zircaloy cladding, respectively, was investigated and compared under both normal operating and accident conditions. Compared with the UO2 fuel, the Th0.923U0.077O2 and Th0.923Pu0.077O2 fuels were found to increase the fuel centerline temperature under both normal operating and reactivity-initiated accident (RIA) conditions, but decrease the fuel centerline temperature under loss-of-coolant accident (LOCA) condition. Moreover, compared to the UO2 fuel with the Zircaloy cladding, thorium-based fuels with Cr-coated SiC/SiC composite cladding were found to show better mechanical performance such as delaying the failure time by about 3 s of the Cr-coated SiC/SiC composite cladding under LOCA condition, and reducing the plenum pressure by about 0.4 MPa at the peak value in the fuel rod and the hoop strain of the cladding by about 16% under RIA condition.

scholarly journals The Effect of Estimating the Shape Parameter on Probability Distributions Using the Moment Method

2018 ◽  
Vol 2 (3) ◽  
Author(s):  
Hamza Ibrahim Hamza
Keyword(s):  
Shape Parameter ◽  
Probability Distributions ◽  
Estimation Method ◽  
Simulation Method ◽  
Inductive Method ◽  
Binomial Distributions ◽  
Matlab Program ◽  
Best Estimate ◽  
The Mean ◽  
The Moment

  The purpose of this paper was to identify the values ​​of the parameters of the shape of the binomial, Poisson and natural distributions. Using the estimation method, the criterion of differentiation was used to estimate the shape parameter between the probability distributions and to arrive at the best estimate of the parameter of the shape when the sample sizes are small, medium, The problem was to find the best estimate of the characteristics of the society to be estimated so that they are close to the estimated average of the mean error squares and also the effect of the estimation method on estimating the shape parameter of the distributions at the sizes of different samples In the values ​​of the different shape parameter, the descriptive and inductive method was selected in the analysis of the data by generating 1000 random numbers of different sizes using the simulation method through the MATLAB program A number of results were reached, 10) to estimate the small shape parameter (0.3) for binomial distributions, Poisson and natural and they can use the Poisson distribution because it is the best among the distributions, and to estimate the parameter of figure (0.5), (0.7), (0.9) Because it is better for binomial binomial distributions, when the size of a sample (70) for a teacher estimate The small figure (0.3) of the binomial and boson distributions and natural distributions can be used for normal distribution because it is the best among the distributions. For estimating the parameter of figure (0.5), (0.7), (0.9) Among distributions. The paper also issued a number of recommendations, most notably the use of binomial distribution to estimate the parameter of the figure (0.9) at the size of sample (10), (30), (50), (70).  

Ratcheting assessment of corroded elbow pipes subjected to internal pressure and cyclic bending moment

2021 ◽  
pp. 030932472198989
Author(s):  
Ali Salehi ◽  
Armin Rahmatfam ◽  
Mohammad Zehsaz
Keyword(s):  
Growth Rate ◽  
Stainless Steel ◽  
Internal Pressure ◽  
Bending Moment ◽  
Axial Direction ◽  
Hoop Strain ◽  
Cyclic Bending ◽  
High Fatigue ◽  
The Impact ◽  
Cyclic Bending Moment

The present study aimed to study ratcheting strains of corroded stainless steel 304LN elbow pipes subjected to internal pressure and cyclic bending moment. To this aim, spherical and cubical shapes corrosion are applied at two depths of 1 mm and 2 mm in the critical points of elbow pipe such as symmetry sites at intrados, extrados, and crown positions. Then, a Duplex 2205 stainless steel elbow pipe is considered as an alternative to studying the impact of the pipe materials, due to its high corrosion resistance and strength, toughness, and most importantly, the high fatigue strength and other mechanical properties than stainless steel 304LN. In order to perform numerical analyzes, the hardening coefficients of the materials were calculated. The results highlight a significant relationship between the destructive effects of corrosion and the depth and shape of corrosion, so that as corrosion increases, the resulting destructive effects increases as well, also, the ratcheting strains in cubic corrosions have a higher growth rate than spherical corrosions. In addition, the growth rate of the ratcheting strains in the hoop direction is much higher across the studied sample than the axial direction. The highest growth rate of hoop strain was observed at crown and the highest growth rate of axial strains occurred at intrados position. Altogether, Duplex 2205 material has a better performance than SS 304LN.

Co-localization analysis in fluorescence microscopy via maximum entropy copula

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Zahra Amini Farsani ◽  
Volker J. Schmid
Keyword(s):  
Fluorescence Microscopy ◽  
Maximum Entropy ◽  
Probability Distributions ◽  
Real Data ◽  
Bivariate Distribution ◽  
Entropy Method ◽  
Gaussian Copula ◽  
Microscopy Imaging ◽  
High Background ◽  
Localization Analysis

AbstractCo-localization analysis is a popular method for quantitative analysis in fluorescence microscopy imaging. The localization of marked proteins in the cell nucleus allows a deep insight into biological processes in the nucleus. Several metrics have been developed for measuring the co-localization of two markers, however, they depend on subjective thresholding of background and the assumption of linearity. We propose a robust method to estimate the bivariate distribution function of two color channels. From this, we can quantify their co- or anti-colocalization. The proposed method is a combination of the Maximum Entropy Method (MEM) and a Gaussian Copula, which we call the Maximum Entropy Copula (MEC). This new method can measure the spatial and nonlinear correlation of signals to determine the marker colocalization in fluorescence microscopy images. The proposed method is compared with MEM for bivariate probability distributions. The new colocalization metric is validated on simulated and real data. The results show that MEC can determine co- and anti-colocalization even in high background settings. MEC can, therefore, be used as a robust tool for colocalization analysis.

scholarly journals A Probability Density Function Generator Based on Deep Learning

2018 ◽  
Author(s):  
Chi-Hua Chen ◽  
Fangying Song ◽  
Feng-Jang Hwang ◽  
Ling Wu
Keyword(s):  
Deep Learning ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Probability Distributions ◽  
Real Data ◽  
Learning Model ◽  
Cumulative Distribution ◽  
Function Generator ◽  
Deep Learning Model

To generate a probability density function (PDF) for fitting probability distributions of real data, this study proposes a deep learning method which consists of two stages: (1) a training stage for estimating the cumulative distribution function (CDF) and (2) a performing stage for predicting the corresponding PDF. The CDFs of common probability distributions can be adopted as activation functions in the hidden layers of the proposed deep learning model for learning actual cumulative probabilities, and the differential equation of trained deep learning model can be used to estimate the PDF. To evaluate the proposed method, numerical experiments with single and mixed distributions are performed. The experimental results show that the values of both CDF and PDF can be precisely estimated by the proposed method.

scholarly journals Empirical Bayesian regression model for estimation of small rates

2012 ◽  
Vol 53 ◽  
Author(s):  
Gintautas Jakimauskas ◽  
Leonidas Sakalauskas
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Population Data ◽  
Real Data ◽  
Simulation Method ◽  
Bayesian Regression ◽  
Distribution Model ◽  
Estimation Model ◽  
Hospital Discharges ◽  
Large Populations

The efficiency of adding an auxiliary regression variable to the logit model in estimation of small probabilities in large populations is considered. Let us consider two models of distribution of unknown probabilities: the probabilities have gamma distribution (model (A)), or logits of the probabilities have Gaussian distribution (model (B)). In modification of model (B) we will use additional regression variable for Gaussian mean (model (BR)). We have selected real data from Database of Indicators of Statistics Lithuania – Working-age persons recognized as disabled for the first time by administrative territory, year 2010 (number of populations K = 60). Additionally, we have used average annual population data by administrative territory. The auxiliary regression variable was based on data – Number of hospital discharges by administrative territory, year 2010. We obtained initial parameters using simple iterative procedures for models (A), (B) and (BR). At the second stage we performed various tests using Monte-Carlo simulation (using models (A), (B) and (BR)). The main goal was to select an appropriate model and to propose some recommendations for using gamma and logit (with or without auxiliary regression variable) models for Bayesian estimation. The results show that a Monte Carlo simulation method enables us to determine which estimation model is preferable.

scholarly journals Technical-Economic Analysis of Grapple Saw

2020 ◽  
Vol 41 (2) ◽  
pp. 219-229 ◽  
Author(s):  
Ricardo Hideaki Miyajima ◽  
Paulo Torres Fenner ◽  
Gislaine Cristina Batistela ◽  
Danilo Simões
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Probability Distributions ◽  
Simulation Method ◽  
Forest Harvesting ◽  
Production Costs ◽  
Wood Harvesting ◽  
Food And Agriculture ◽  
The Monte Carlo Method

The processing of Eucalyptus logs is a stage that follows the full tree system in mechanized forest harvesting, commonly performed by grapple saw. Therefore, this activity presents some associated uncertainties, especially regarding technical and silvicultural factors that can affect productivity and production costs. To get around this problem, Monte Carlo simulation can be applied, or rather a technique that allows to measure the probabilities of values from factors that are under conditions of uncertainties, to which probability distributions are attributed. The objective of this study was to apply the Monte Carlo method for determining the probabilistic technical-economical coefficients of log processing using two different grapple saw models. Field data were obtained from an area of forest planted with Eucalyptus, located in the State of São Paulo, Brazil. For the technical analysis, the time study protocol was applied by the method of continuous reading of the operational cycle elements, which resulted in production. As for the estimated cost of programmed hour, the applied methods were recommended by the Food and Agriculture Organization of the United Nations. The incorporation of the uncertainties was carried out by applying the Monte Carlo simulation method, by which 100,000 random values were generated. The results showed that the crane empty movement is the operational element that most impacts the total time for processing the logs; the variables that most influence the productivity are specific to each grapple saw model; the difference of USD 0.04 m3 in production costs was observed between processors with gripping area of 0.58 m2 and 0.85 m2. The Monte Carlo method proved to be an applicable tool for mechanized wood harvesting for presenting a range of probability of occurrences for the operational elements and for the production cost.

Identification of Forming Limits for Unidirectional Carbon Textiles in Reality and Mesoscopic Simulation

2013 ◽  
Vol 554-557 ◽  
pp. 423-432 ◽  
Author(s):  
Patrick Böhler ◽  
Frank Härtel ◽  
Peter Middendorf
Keyword(s):  
Raw Materials ◽  
Weight Ratio ◽  
Experimental Tests ◽  
Simulation Method ◽  
Failure Criteria ◽  
Forming Process ◽  
Mesoscopic Simulation ◽  
Sewing Thread ◽  
Young’S Moduli ◽  
Definition Of

In several fields of engineering the use of carbon fibre reinforced material (CFRP) is increasing. Minimized weight due to CFRPs could lead to lower consumption of raw materials especially in the automotive area. The goal within the research project TC² is the decrease of costs and production time for composite materials. To achieve better performance to weight ratio and to get acceptable production conditions the draping of dry unidirectional textiles and a following RTM process is investigated. Due to the high degree of complexity of automotive structures the forming process is challenging. Gapping in the textile could appear at corners as well as wrinkling or flexion of the fibres. To be able to define the amount and direction of layers or patches it is necessary to know the limits of forming for unidirectional material and to be able to predict the behaviour of the textile during the forming process. For the definition of the process limits several draping strategies are performed on different corner blend geometries. The goal of that work is to define the critical gradient of the flange to get first failures such as wrinkling or gapping. It is also important to understand the influence of different draping strategies. Parallel to the experimental tests a mesoscopic simulation method using an approach with roving and sewing thread is developed and presented. It is able to predict the material behaviour in critical areas (gapping, wrinkling). Different Young’s moduli and failure criteria can be implemented for the two main directions as well as for the bending of the textile. A validation with the experimental results is performed with the aim to enable the prediction of the textile behaviour using simulation methods.

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