Estimating Weibull Parameters Using Least Squares and Multilayer Perceptron vs. Bayes Estimation

Aydi, Walid; Al-Duais, Fuad S.

doi:10.32604/cmc.2022.023119

Cited by 6 publications

(3 citation statements)

References 38 publications

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“…To account for the differences (errors) observed in the mathematical model, the x and y data will be considered as realizations of two random variables, X and Y. The principle of the least squares method (LSM) consists in choosing the values of a and b, which minimize the squares of the deviations given by Equation (1) [34,35]:…”

Section: Least Square Methods (Lsm)mentioning

confidence: 99%

Effect of the stochastic weibull parameters on the reliability of the dialysis machine

Fenina,

Jendoubi,

Bouchoucha

2024

ETJ

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 The Weibull parameters were calculated using several methods  The uncertainties of the shape and scale parameters were estimated  The random failure rate and reliability of the dialysis devices were studied  The systematic inspection period of the dialysis devices was estimated in a stochastic environment Dialysis machines operate in an uncertain environment with several sources of disturbances; therefore, it is necessary to take account of the uncertainties during all their life phases. This paper presents a study of the random reliability of the dialysis machine in a stochastic environment through the two-parameter for Weibull distribution. The shape and scale parameters were estimated through analytical and graphical methods based on the failure history of the devices. The formulation of the analytical methods and their exploitation using numerical simulations was one of the objectives of this work. The uncertainties in the stochastic environment of the machines are related to variability in physical and geometric parameters, fluctuations in load conditions, stress boundary conditions, and also to physical laws and simplifying assumptions used in the modeling process. The Weibull parameters introduced these uncertainties, and their effect on the device's reliability was studied. The main contribution is the study of the effect of the uncertainties in Weibull parameters on the reliability of the dialysis machine. The question of the uncertainties in the Weibull parameters was treated. The involved parameters were considered a Gaussian variable, and their means and standard deviations were calculated in several configurations of the dialysis devices. The random failure rate and reliability were treated and discussed. The random systematic inspection period is studied to install an efficient preventive maintenance program.

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Section: Least Square Methods (Lsm)mentioning

confidence: 99%

Effect of the stochastic weibull parameters on the reliability of the dialysis machine

Fenina,

Jendoubi,

Bouchoucha

2024

ETJ

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“…Therefore, to fix the estimation problem, we adopt a Markov chain Monte Carlo (MCMC) method, which can sample from a simple conditional distribution of a stable Markov chain [22], instead of a complicated target PDF. Since the conditional distribution is difficult to choose, the Metropolis-Hastings (M-H) method [23][24][25][26][27] is proposed, which draw samples from any simple distributions with a constraint of an acceptance ratio [28]. As only the conditional PDF of a stable Markov chain corresponds to the target PDF, the convergence of the chain influences the computational complexity of the proposed method.…”

Section: Introductionmentioning

confidence: 99%

Robust Frequency Estimation Under Additive Symmetric α-Stable Gaussian Mixture Noise

Wang¹,

Tian²,

Men³

et al. 2023

Intelligent Automation &Amp; Soft Computing

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Here the estimating problem of a single sinusoidal signal in the additive symmetric α-stable Gaussian (ASαSG) noise is investigated. The ASαSG noise here is expressed as the additive of a Gaussian noise and a symmetric α-stable distributed variable. As the probability density function (PDF) of the ASαSG is complicated, traditional estimators cannot provide optimum estimates. Based on the Metropolis-Hastings (M-H) sampling scheme, a robust frequency estimator is proposed for ASαSG noise. Moreover, to accelerate the convergence rate of the developed algorithm, a new criterion of reconstructing the proposal covariance is derived, whose main idea is updating the proposal variance using several previous samples drawn in each iteration. The approximation PDF of the ASαSG noise, which is referred to the weighted sum of a Voigt function and a Gaussian PDF, is also employed to reduce the computational complexity. The computer simulations show that the performance of our method is better than the maximum likelihood and the lp-norm estimators.

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“…At present, the main methods of estimating parameters of Weibull distribution are statistical estimation method, 8,9 gray estimation method, 10,11 maximum likelihood method, 12–15 genetic algorithm, 16–20 and right approximation method. 21–27 These methods have different adaptability to different sample sizes, but basically all of them have high requirements on the initial value of iteration and need to go through complex calculations.…”

Section: Introductionmentioning

confidence: 99%

Research on parameter estimation methods of fatigue life distribution model of automotive chassis parts

Liu

et al. 2022

Advances in Mechanical Engineering

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The reliability assessment of fatigue life of automotive chassis parts is an important part of automobile safety. The fatigue endurance tests of automotive half-axles were carried out. The three-parameter Weibull distribution model was established according to the fatigue life distribution of samples. Using the right approximation method and the genetic algorithm to estimate three parameters of the distribution model and a comparative analysis was made. The results show that the initial life unreliability estimated by the median rank in the right approximation method had a large deviation from the true value, which may cause the iterative algorithm fall into the local optimal solution and affect the estimation accuracy. Therefore, a new parameter estimation method based on dual genetic algorithm was proposed. The newly proposed dual genetic algorithm not only improves the iteration speed, but also improves the accuracy of parameter estimation, which provides new ideas and theoretical basis for reliability assessment of mechanical components.

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Estimating Weibull Parameters Using Least Squares and Multilayer Perceptron vs. Bayes Estimation

Cited by 6 publications

References 38 publications

Effect of the stochastic weibull parameters on the reliability of the dialysis machine

Effect of the stochastic weibull parameters on the reliability of the dialysis machine

Robust Frequency Estimation Under Additive Symmetric α-Stable Gaussian Mixture Noise

Research on parameter estimation methods of fatigue life distribution model of automotive chassis parts

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