scholarly journals Nonparametric Modeling of Random Uncertainties for Dynamic Response of Mistuned Bladed Disks

2004 ◽  
Vol 126 (3) ◽  
pp. 610-618 ◽  
Author(s):  
E. Capiez-Lernout ◽  
C. Soize
Keyword(s):  
Probability Model ◽  
Nonparametric Model ◽  
Probability Models ◽  
Nonparametric Modeling ◽  
Modal Shape ◽  
New Approach ◽  
Nonlinear Elastodynamics ◽  
Optimization Principle ◽  
Random Character ◽  
Random Uncertainties

The random character of blade mistuning is a motivation to construct probability models of random uncertainties. Recently, a new approach known as a nonparametric model of random uncertainties, based on the entropy optimization principle, was introduced for modeling random uncertainties in linear and nonlinear elastodynamics. This paper presents an extension of this nonparametric model for vibration analysis of structures with cyclic geometry. In particular this probability model allows the blade eigenfrequencies uncertainties and the blade-modal-shape uncertainties to be modeled.

scholarly journals A new approach for modeling covid-19 death data

2021 ◽  
pp. 1-9
Author(s):  
Muhammad Farooq ◽  
Qamar-uz-zaman ◽  
Muhammad Ijaz
Keyword(s):  
Probability Model ◽  
Developed Countries ◽  
Likelihood Method ◽  
Data Sets ◽  
Probability Models ◽  
New Approach ◽  
Proposed Model ◽  
Rate Functions ◽  
Day By Day ◽  
Death Data

The Covid-19 infections outbreak is increasing day by day and the mortality rate is increasing exponentially both in underdeveloped and developed countries. It becomes inevitable for mathematicians to develop some models that could define the rate of infections and deaths in a population. Although there exist a lot of probability models but they fail to model different structures (non-monotonic) of the hazard rate functions and also do not provide an adequate fit to lifetime data. In this paper, a new probability model (FEW) is suggested which is designed to evaluate the death rates in a Population. Various statistical properties of FEW have been screened out in addition to the parameter estimation by using the maximum likelihood method (MLE). Furthermore, to delineate the significance of the parameters, a simulation study is conducted. Using death data from Pakistan due to Covid-19 outbreak, the proposed model applications is studied and compared to that of other existing probability models such as Ex-W, W, Ex, AIFW, and GAPW. The results show that the proposed model FEW provides a much better fit while modeling these data sets rather than Ex-W, W, Ex, AIFW, and GAPW.

A new approach to bracket prediction in the NCAA Men’s Basketball Tournament based on a dual-proportion likelihood

2015 ◽  
Vol 11 (1) ◽  
Author(s):  
Ajay Andrew Gupta
Keyword(s):  
National Collegiate Athletic Association ◽  
Expert Knowledge ◽  
Probability Model ◽  
Expected Value ◽  
Division I ◽  
Prediction System ◽  
New Approach ◽  
Men's Basketball ◽  
Popular Interest ◽  
The One

AbstractThe widespread proliferation of and interest in bracket pools that accompany the National Collegiate Athletic Association Division I Men’s Basketball Tournament have created a need to produce a set of predicted winners for each tournament game by people without expert knowledge of college basketball. Previous research has addressed bracket prediction to some degree, but not nearly on the level of the popular interest in the topic. This paper reviews relevant previous research, and then introduces a rating system for teams using game data from that season prior to the tournament. The ratings from this system are used within a novel, four-predictor probability model to produce sets of bracket predictions for each tournament from 2009 to 2014. This dual-proportion probability model is built around the constraint of two teams with a combined 100% probability of winning a given game. This paper also performs Monte Carlo simulation to investigate whether modifications are necessary from an expected value-based prediction system such as the one introduced in the paper, in order to have the maximum bracket score within a defined group. The findings are that selecting one high-probability “upset” team for one to three late rounds games is likely to outperform other strategies, including one with no modifications to the expected value, as long as the upset choice overlaps a large minority of competing brackets while leaving the bracket some distinguishing characteristics in late rounds.

Study on Hazard Analysis Method of Earthquake Secondary Fire Disaster in Urban Area Based on GIS

2012 ◽  
Vol 204-208 ◽  
pp. 3457-3461
Author(s):  
Tian Qi Li ◽  
Fei Geng
Keyword(s):  
Urban Areas ◽  
Hazard Analysis ◽  
Probability Model ◽  
Probability Models ◽  
Housing Density ◽  
Earthquake Excitation ◽  
Fire Disaster ◽  
High Hazard ◽  
The City ◽  
And Diffusion

In order to study the probability of occurrence of secondary fire after the earthquake in urban areas, the probability model of the hazard analysis that the fire occurred and the spread is established and applied. Probability models need to consider the destruction level of buildings under earthquake excitation as well as the probability of the leakage and diffusion of combustible material in the buildings in the corresponding destruction level, combination of weather, season, housing density and other factors to determine the probability of the single building earthquake secondary fire. On this basis , the natural administrative areas in the city as a unit , considering the factors of regional hazard analysis such as population density , property distribution and density within a region , to calculate the hazard indicator and determine the high hazard areas of secondary fire in the city. The Geographic Information System was used as the platform, to division of urban earthquake secondary fire high-hazard areas.

The wave finite element method for uncertain systems with model uncertainty

2015 ◽  
Vol 230 (6) ◽  
pp. 974-985 ◽  
Author(s):  
MA Ben Souf ◽  
O Bareille ◽  
M Ichchou ◽  
M Haddar
Keyword(s):  
Finite Element ◽  
Dynamic Systems ◽  
Periodic Structures ◽  
Probabilistic Approach ◽  
Numerical Test ◽  
Maximum Entropy Principle ◽  
Nonparametric Model ◽  
Test Cases ◽  
Entropy Principle ◽  
Random Uncertainties

The random dynamic response of periodic structures with model uncertainties is here studied. For that purpose, a nonparametric model of random uncertainties is used. The present approach is based on the maximum entropy principle optimization and is developed to identify the response of linear and nonlinear dynamic systems. This non-parametric probabilistic approach is implemented in combination with the Wave Finite Element. Numerical test cases are used as examples and for validation purpose.

scholarly journals On the S-instability and degeneracy of discrete deep learning models

2019 ◽  
Vol 9 (3) ◽  
pp. 627-655 ◽  
Author(s):  
Andee Kaplan ◽  
Daniel J Nordman ◽  
Stephen B Vardeman
Keyword(s):  
Probability Model ◽  
Correlated Data ◽  
Data Sequence ◽  
Probability Models ◽  
Large Classes ◽  
Learning Contexts ◽  
Probability Structure ◽  
Model Probability ◽  
Parameter Sequence ◽  
Outcome Result

Abstract A probability model exhibits instability if small changes in a data outcome result in large and, often unanticipated, changes in probability. This instability is a property of the probability model, given by a distributional form and a given configuration of parameters. For correlated data structures found in several application areas, there is increasing interest in identifying such sensitivity in model probability structure. We consider the problem of quantifying instability for general probability models defined on sequences of observations, where each sequence of length $N$ has a finite number of possible values that can be taken at each point. A sequence of probability models, indexed by $N$, and an associated parameter sequence result to accommodate data of expanding dimension. Model instability is formally shown to occur when a certain log probability ratio under such models grows faster than $N$. In this case, a one component change in the data sequence can shift probability by orders of magnitude. Also, as instability becomes more extreme, the resulting probability models are shown to tend to degeneracy, placing all their probability on potentially small portions of the sample space. These results on instability apply to large classes of models commonly used in random graphs, network analysis and machine learning contexts.

scholarly journals Bayesian Nonparametric Modeling for Rapid Design of Metamaterial Microstructures

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Bin Liu ◽  
Chunlin Ji
Keyword(s):  
Geometric Dimension ◽  
Mapping Function ◽  
Point Of View ◽  
Electromagnetic Response ◽  
Type Model ◽  
Nonparametric Model ◽  
Bayesian Nonparametric ◽  
Nonparametric Modeling ◽  
Statistical Point ◽  
Rapid Design

We consider the problem of rapid design of massive metamaterial (MTM) microstructures from a statistical point of view. A Bayesian nonparametric model, namely, Gaussian Process (GP) mixture, is developed to generate the mapping relationship from the microstructure’s geometric dimension to the electromagnetic response, which is approximately expressed in a closed form of Drude-Lorentz type model. This GP mixture model is neatly able to tackle nonstationarity, discontinuities in the mapping function. The inference is performed using a Markov chain relying on Gibbs sampling. Experimental results demonstrate that the proposed approach is highly efficient in facilitating rapid design of MTM with accuracy.

scholarly journals Bell Could Become the Copernicus of Probability

2016 ◽  
Vol 23 (02) ◽  
pp. 1650008 ◽  
Author(s):  
Andrei Khrennikov
Keyword(s):  
Probability Model ◽  
Quantum Probability ◽  
Bell’S Inequality ◽  
Probability Models ◽  
Bell's Inequality ◽  
Mathematical Probability ◽  
Model Interpretation ◽  
Born’S Rule ◽  
Quantum Phenomena

Our aim is to emphasize the role of mathematical models in physics, especially models of geometry and probability. We briefly compare developments of geometry and probability by pointing to similarities and differences: from Euclid to Lobachevsky and from Kolmogorov to Bell. In probability, Bell could play the same role as Lobachevsky in geometry. In fact, violation of Bell’s inequality can be treated as implying the impossibility to apply the classical probability model of Kolmogorov (1933) to quantum phenomena. Thus the quantum probabilistic model (based on Born’s rule) can be considered as the concrete example of the non-Kolmogorovian model of probability, similarly to the Lobachevskian model — the first example of the non-Euclidean model of geometry. This is the “probability model” interpretation of the violation of Bell’s inequality. We also criticize the standard interpretation—an attempt to add to rigorous mathematical probability models additional elements such as (non)locality and (un)realism. Finally, we compare embeddings of non-Euclidean geometries into the Euclidean space with embeddings of the non-Kolmogorovian probabilities (in particular, quantum probability) into the Kolmogorov probability space. As an example, we consider the CHSH-test.

scholarly journals Specifying Manufacturing Tolerances for a Given Amplification Factor: A Nonparametric Probabilistic Methodology

2003 ◽  
Author(s):  
Evange´line Capiez-Lernout ◽  
Christian Soize
Keyword(s):  
Inverse Problem ◽  
Probabilistic Model ◽  
Amplification Factor ◽  
Forced Response ◽  
Bladed Disks ◽  
Nonparametric Approach ◽  
Modeling Errors ◽  
Random Character ◽  
Manufacturing Tolerances ◽  
Random Uncertainties

It is known that the forced response of mistuned bladed disks can strongly be amplified in comparison with the forced response of the tuned system. The random character of mistuning thus requires the construction of probabilistics models of random uncertainties. This paper presents a nonparametric probabilistic model of random uncertainties which is adapted to the problematics of the blade mistuning. This nonparametric approach allows all the uncertainties yielding mistuning (manufacturing tolerances, dispersion of materials) to be taken into account and includes also the uncertainties due to the modeling errors. This new probabilistic model takes into account both the mistuning of the blade eigenfrequencies and the blade modal shapes. The first point concerns the construction of this nonparametric approach in order to perform a mistuning analysis. The second part is devoted to the inverse problem associated with the manufacturing tolerances. A relationship between the manufacturing tolerances and the level of mistuning is also constructed.

scholarly journals Factors Influencing the Performance of Regression-Based Statistical Postprocessing Models for Short-Term Precipitation Forecasts

2019 ◽  
Vol 34 (6) ◽  
pp. 2067-2084
Author(s):  
Wentao Li ◽  
Qingyun Duan ◽  
Quan J. Wang
Keyword(s):  
Prediction Models ◽  
Probability Model ◽  
Weather Prediction ◽  
Joint Probability ◽  
Ensemble Spread ◽  
Probability Models ◽  
Short Term ◽  
Huai River ◽  
Censored Regression Model ◽  
Distributional Regression

Abstract Statistical postprocessing models can be used to correct bias and dispersion errors in raw precipitation forecasts from numerical weather prediction models. In this study, we conducted experiments to investigate four factors that influence the performance of regression-based postprocessing models with normalization transformations for short-term precipitation forecasts. The factors are 1) normalization transformations, 2) incorporation of ensemble spread as a predictor in the model, 3) objective function for parameter inference, and 4) two postprocessing schemes, including distributional regression and joint probability models. The experiments on the first three factors are based on variants of a censored regression model with conditional heteroscedasticity (CRCH). For the fourth factor, we compared CRCH as an example of the distributional regression with a joint probability model. The results show that the CRCH with normal quantile transformation (NQT) or power transformation performs better than the CRCH with log–sinh transformation for most of the subbasins in Huai River basin with a subhumid climate. The incorporation of ensemble spread as a predictor in CRCH models can improve forecast skill in our research region at short lead times. The influence of different objective functions (minimum continuous ranked probability score or maximum likelihood) on postprocessed results is limited to a few relatively dry subbasins in the research region. Both the distributional regression and the joint probability models have their advantages, and they are both able to achieve reliable and skillful forecasts.

scholarly journals Spatial probability modelling of eelgrass (Zostera marina) distribution on the west coast of Norway

2008 ◽  
Vol 65 (7) ◽  
pp. 1093-1101 ◽  
Author(s):  
Trine Bekkby ◽  
Eli Rinde ◽  
Lars Erikstad ◽  
Vegar Bakkestuen ◽  
Oddvar Longva ◽  
...  
Keyword(s):  
West Coast ◽  
Zostera Marina ◽  
Probability Model ◽  
Probability Models ◽  
The West ◽  
Spatial Probability ◽  
Marine Habitats ◽  
Predictive Probability ◽  
Field Samples ◽  
Probability Modelling

Abstract Bekkby, T., Rinde, E., Erikstad, L., Bakkestuen, V., Longva, O., Christensen, O., Isæus, M., and Isachsen, P. E. 2008. Spatial probability modelling of eelgrass (Zostera marina) distribution on the west coast of Norway. – ICES Journal of Marine Science, 65: 1093–1101. Based on modelled and measured geophysical variables and presence/absence data of eelgrass Zostera marina, we developed a spatial predictive probability model for Z. marina. Our analyses confirm previous reports and show that the probability of finding Z. marina is at its highest in shallow, gently sloping, and sheltered areas. We integrated the empirical knowledge from field samples in GIS and developed a model-based map of the probability of finding Z. marina using the model-selection approach Akaike Information Criterion (AIC) and the spatial probability modelling extension GRASP in S-Plus. Spatial predictive probability models contribute to a better understanding of the factors and processes structuring the distribution of marine habitats. Additionally, such models provide a useful tool for management and research, because they are quantitative and defined objectively, extrapolate knowledge from sampled to unsurveyed areas, and result in a probability map that is easy to understand and disseminate to stakeholders.

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