Staff View: A novel q-exponential based stress-strength reliability model and applications to fatigue life with extreme values

A novel q-exponential based stress-strength reliability model and applications to fatigue life with extreme values

In recent years, a family of probability distributions based on Nonextensive Statistical Mechanics, known as q-distributions, has experienced a surge in terms of applications to several fields of science and engineering. In this work the _-Exponential distribution will be studied in detail. One o...

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Main Author:	SALES FILHO, Romero Luiz Mendonça
Other Authors:	DROGUETT, Enrique López
Format:	doctoralThesis
Language:	eng
Published:	Universidade Federal de Pernambuco 2016
Subjects:	Q-Exponencial Confiabilidade Força-Estresse Estimador de Máxima Verossimilhaça Nelder-Mead Particle Swarm Optimization
Online Access:	https://repositorio.ufpe.br/handle/123456789/17632
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spelling	ir-123456789-176322018-09-27T22:26:10Z A novel q-exponential based stress-strength reliability model and applications to fatigue life with extreme values SALES FILHO, Romero Luiz Mendonça DROGUETT, Enrique López http://lattes.cnpq.br/4252707165390630 http://lattes.cnpq.br/7731672359030872 Q-Exponencial Confiabilidade Força-Estresse Estimador de Máxima Verossimilhaça Nelder-Mead Particle Swarm Optimization Q-Exponencial Confiabilidade Força-Estresse Estimador de Máxima Verossimilhaça Nelder-Mead Particle Swarm Optimization In recent years, a family of probability distributions based on Nonextensive Statistical Mechanics, known as q-distributions, has experienced a surge in terms of applications to several fields of science and engineering. In this work the _-Exponential distribution will be studied in detail. One of the features of this distribution is the capability of modeling data that have a power law behavior, since it has a heavy-tailed probability density function (PDF) for particular values of its parameters. This feature allows us to consider this distribution as a candidate to model data sets with extremely large values (e.g. cycles to failure). Once the analytical expressions for the maximum likelihood estimates (MLE) of _-Exponential are very difficult to be obtained, in this work, we will obtain the MLE for the parameters of the _- Exponential using two different optimization methods: particle swarm optimization (PSO) and Nelder-Mead (NM), which are also coupled with parametric and non-parametric bootstrap methods in order to obtain confidence intervals for these parameters; asymptotic intervals are also derived. Besides, we will make inference about a useful performance metric in system reliability, the called index _􀀃_(_􀀇􀀈􀀉, where the stress _ and strength 􀀈 are independent q-Exponential random variables with different parameters. In fact, when dealing with practical problems of stress-strength reliability, one can work with fatigue life data and make use of the well-known relation between stress and cycles until failure. For some materials, this kind of data can involve extremely large values and the capability of the q- Exponential distribution to model data with extremely large values makes this distribution a good candidate to adjust stress-strength models. In terms of system reliability, the index _ is considered a topic of great interest, so we will develop the maximum likelihood estimator (MLE) for the index _ and show that this estimator is obtained by a function that depends on the parameters of the distributions for 􀀈 and _. The behavior of the MLE for the index _ is assessed by means of simulated experiments. Moreover, confidence intervals are developed based on parametric and non-parametric bootstrap. As an example of application, we consider two experimental data sets taken from literature: the first is related to the analysis of high cycle fatigue properties of ductile cast iron for wind turbine components, and the second one evaluates the specimen size effects on gigacycle fatigue properties of high-strength steel. CAPEs Nos últimos anos, tem sido notado em diversas áreas da ciência e engenharia, um aumento significativo na aplicabilidade da família q de distribuições de probabilidade que se baseia em Mecânica Estatística Não Extensiva. Uma das características da distribuição q-Exponencial é a capacidade de modelar dados que apresentam comportamento de lei de potência, uma vez que tal distribuição possui uma função densidade de probabilidade (FDP) que apresenta cauda pesada para determinados valores de parâmetros. Esta característica permite-nos considerar tal distribuição como candidata para modelar conjuntos de dados que apresentam valores extremamente grandes (Ex.: ciclos até a falha). Uma vez que expressões analíticas para os estimadores de máxima verossimilhança dos parâmetros não são facilmente encontradas, neste trabalho, iremos obter as estimativas de máxima verossimilhança dos parâmetros através de dois métodos de otimização: particle swarm optimization (PSO) e Nelder-Mead (NM), que além das estimativas pontuais, irão nos fornecer juntamente com abordagens bootstrap, intervalos de confiança para os parâmetros da distribuição; intervalos assintóticos também serão derivados. Além disso, faremos inferência sobre um importante índice de confiabilidade, o chamado Índice _􀀃_(_􀀇􀀈􀀉, onde Y (estresse) e X (força) são variáveis aleatórias independentes. De fato, quando tratamos de problemas práticos de força-estresse, podemos trabalhar com dados de fadiga e fazer uso da bem conhecida relação entre estresse e ciclos até a falha. Para alguns materiais, esse tipo de variável pode apresentar dados com valores muito grandes e a capacidade da q-Exponencial em modelar esse tipo de dado torna essa uma distribuição a ser considerada para ajustar modelos de força-estresse. Em termos de confiabilidade de sistemas, o índice R é considerado um tópico de bastante interesse, assim iremos desenvolver os estimadores de máxima verossimilhança para esse índice e mostrar que esse estimador é obtido através de uma função que depende dos parâmetros da distribuição de X e Y. O comportamento do estimador é investigado através de experimentos simulados. Intervalos de confiança são desenvolvidos através de bootstrap paramétrico e nãoparamétrico. Duas aplicações envolvendo dados de ciclos até a falha e retiradas da literatura são consideradas: a primeira para ferro fundido e a segunda para aço de alta resistência. 2016-08-05T14:42:09Z 2016-08-05T14:42:09Z 2016-02-24 doctoralThesis https://repositorio.ufpe.br/handle/123456789/17632 eng Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ Universidade Federal de Pernambuco UFPE Brasil Programa de Pos Graduacao em Engenharia de Producao
institution	REPOSITORIO UFPE
collection	REPOSITORIO UFPE
language	eng
topic	Q-Exponencial Confiabilidade Força-Estresse Estimador de Máxima Verossimilhaça Nelder-Mead Particle Swarm Optimization Q-Exponencial Confiabilidade Força-Estresse Estimador de Máxima Verossimilhaça Nelder-Mead Particle Swarm Optimization
spellingShingle	Q-Exponencial Confiabilidade Força-Estresse Estimador de Máxima Verossimilhaça Nelder-Mead Particle Swarm Optimization Q-Exponencial Confiabilidade Força-Estresse Estimador de Máxima Verossimilhaça Nelder-Mead Particle Swarm Optimization SALES FILHO, Romero Luiz Mendonça A novel q-exponential based stress-strength reliability model and applications to fatigue life with extreme values
description	In recent years, a family of probability distributions based on Nonextensive Statistical Mechanics, known as q-distributions, has experienced a surge in terms of applications to several fields of science and engineering. In this work the _-Exponential distribution will be studied in detail. One of the features of this distribution is the capability of modeling data that have a power law behavior, since it has a heavy-tailed probability density function (PDF) for particular values of its parameters. This feature allows us to consider this distribution as a candidate to model data sets with extremely large values (e.g. cycles to failure). Once the analytical expressions for the maximum likelihood estimates (MLE) of _-Exponential are very difficult to be obtained, in this work, we will obtain the MLE for the parameters of the _- Exponential using two different optimization methods: particle swarm optimization (PSO) and Nelder-Mead (NM), which are also coupled with parametric and non-parametric bootstrap methods in order to obtain confidence intervals for these parameters; asymptotic intervals are also derived. Besides, we will make inference about a useful performance metric in system reliability, the called index _􀀃_(_􀀇􀀈􀀉, where the stress _ and strength 􀀈 are independent q-Exponential random variables with different parameters. In fact, when dealing with practical problems of stress-strength reliability, one can work with fatigue life data and make use of the well-known relation between stress and cycles until failure. For some materials, this kind of data can involve extremely large values and the capability of the q- Exponential distribution to model data with extremely large values makes this distribution a good candidate to adjust stress-strength models. In terms of system reliability, the index _ is considered a topic of great interest, so we will develop the maximum likelihood estimator (MLE) for the index _ and show that this estimator is obtained by a function that depends on the parameters of the distributions for 􀀈 and _. The behavior of the MLE for the index _ is assessed by means of simulated experiments. Moreover, confidence intervals are developed based on parametric and non-parametric bootstrap. As an example of application, we consider two experimental data sets taken from literature: the first is related to the analysis of high cycle fatigue properties of ductile cast iron for wind turbine components, and the second one evaluates the specimen size effects on gigacycle fatigue properties of high-strength steel.
author2	DROGUETT, Enrique López
format	doctoralThesis
author	SALES FILHO, Romero Luiz Mendonça
author_sort	SALES FILHO, Romero Luiz Mendonça
title	A novel q-exponential based stress-strength reliability model and applications to fatigue life with extreme values
title_short	A novel q-exponential based stress-strength reliability model and applications to fatigue life with extreme values
title_full	A novel q-exponential based stress-strength reliability model and applications to fatigue life with extreme values
title_fullStr	A novel q-exponential based stress-strength reliability model and applications to fatigue life with extreme values
title_full_unstemmed	A novel q-exponential based stress-strength reliability model and applications to fatigue life with extreme values
title_sort	novel q-exponential based stress-strength reliability model and applications to fatigue life with extreme values
publisher	Universidade Federal de Pernambuco
publishDate	2016
url	https://repositorio.ufpe.br/handle/123456789/17632
_version_	1641986942358781952
score	13.657419

A novel q-exponential based stress-strength reliability model and applications to fatigue life with extreme values

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