Parameter Estimation of Weibull Distribution Model Based on Ant Colony Algorithm

2014 ◽  
Vol 1070-1072 ◽  
pp. 2073-2078
Author(s):  
Xiu Ji ◽  
Hui Wang ◽  
Chuan Qi Zhao ◽  
Xu Ting Yan
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Ant Colony Algorithm ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Ant Colony ◽  
Likelihood Method ◽  
Distribution Model ◽  
Algorithm Theory

It is difficult to estimate the parameters of Weibull distribution model using maximum likelihood estimation based on particle swarm optimization (PSO) theory for which is easy to fall into premature and needs more variables, ant colony algorithm theory was introduced into maximum likelihood method, and a parameter estimation method based on ant colony algorithm theory was proposed, an example was simulated to verify the feasibility and effectiveness of this method by comparing with ant colony algorithm and PSO.This template explains and demonstrates how to prepare your camera-ready paper for Trans Tech Publications. The best is to read these instructions and follow the outline of this text.

scholarly journals Maximum Likelihood Estimation for Three-Parameter Weibull Distribution Using Evolutionary Strategy

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Fan Yang ◽  
Hu Ren ◽  
Zhili Hu
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Evolutionary Strategy ◽  
Likelihood Method ◽  
Conventional Algorithm

The maximum likelihood estimation is a widely used approach to the parameter estimation. However, the conventional algorithm makes the estimation procedure of three-parameter Weibull distribution difficult. Therefore, this paper proposes an evolutionary strategy to explore the good solutions based on the maximum likelihood method. The maximizing process of likelihood function is converted to an optimization problem. The evolutionary algorithm is employed to obtain the optimal parameters for the likelihood function. Examples are presented to demonstrate the proposed method. The results show that the proposed method is suitable for the parameter estimation of the three-parameter Weibull distribution.

An Improved Parameter Estimation Method for Three-Parameter Weibull Distribution in the Life Analysis of Rolling Bearing

2012 ◽  
Vol 569 ◽  
pp. 442-446 ◽  
Author(s):  
Feng Long Yin ◽  
Ya Shun Wang ◽  
Chun Hua Zhang ◽  
Xiang Po Zhang
Keyword(s):  
Parameter Estimation ◽  
Weibull Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Rolling Bearing ◽  
Accurate Estimate ◽  
Distribution Model ◽  
Bearing Life ◽  
Mechanical Products ◽  
Life Analysis

Three-parameter Weibull distribution is playing a more and more important role in the reliability analysis of mechanical products. It can provide higher accuracy and better reflection of reliability in operating situation concerning fitting and parameter estimation for the rolling bearing life data. This paper focuses on the theory derivation of the maximum likelihood estimation of the three-parameter Weibull distribution, puts forward an improved method for the model parameter estimation and draws the life distribution model. Following that, the method has been proved to be correct and accurate by practical examples.The proposed method can provide a more accurate estimate way for the life analysis of rolling bearing based on three-parameter Weibull distribution.

Maximum Likelihood Method for Parameter Estimation of Weibull Distribution Model Based on Fruit Fly Optimization Algorithm

2014 ◽  
Vol 602-605 ◽  
pp. 3508-3511 ◽  
Author(s):  
Xiang Ping Meng ◽  
Chuan Qi Zhao ◽  
Lei Huo
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Optimization Algorithm ◽  
Likelihood Estimation ◽  
Fruit Fly ◽  
Distribution Model ◽  
Fruit Fly Optimization Algorithm ◽  
Fruit Fly Optimization

It is difficult to estimate the parameters of Weibull distribution model using Maximum Likelihood Estimation based on Ant Colony Algorithm (ACA) or Particle Swarm Optimization theory (PSO) for which is easy to fall into premature and needs more variables, thus Fruit Fly Optimization Algorithm (FOA) theory is introduced into maximum likelihood estimation, and a parameter estimation method based on FOA theory is proposed, an example has been simulated to verify the feasibility and effectiveness of this method by comparing with ACA and PSO.

scholarly journals Selection of Efficient Parameter Estimation Method for Two-Parameter Weibull Distribution

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Mohammed M. A. Almazah ◽  
Muhammad Ismail
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Mean Square Error ◽  
Estimation Method ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Model Parameters ◽  
Mean Square ◽  
Two Parameter

Several studies have considered various scheduling methods and reliability functions to determine the optimum maintenance time. These methods and functions correspond to the lowest cost by using the maximum likelihood estimator to evaluate the model parameters. However, this paper aims to estimate the parameters of the two-parameter Weibull distribution (α, β). The maximum likelihood estimation method, modified linear exponential loss function, and Wyatt-based regression method are used for the estimation of the parameters. Minimum mean square error (MSE) criterion is used to evaluate the relative efficiency of the estimators. The comparison of the different parameter estimation methods is conducted, and the efficiency of these methods is observed, both mathematically and experimentally. The simulation study is conducted for comparison of samples sizes (10, 50, 100, 150) based on the mean square error (MSE). It is concluded that the maximum likelihood method was found to be the most efficient method for all sample sizes used in the research because it achieved the least MSE compared with other methods.

scholarly journals Parameter estimation in a Black Scholes

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 117-122
Author(s):  
Mustafa Bayram ◽  
Buyukoz Orucova ◽  
Tugcem Partal
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Parametric Method ◽  
Estimation Method ◽  
Parametric Estimation ◽  
Likelihood Method ◽  
Observation Data ◽  
Unknown Parameters ◽  
Black Scholes ◽  
Non Parametric

In this paper we discuss parameter estimation in black scholes model. A non-parametric estimation method and well known maximum likelihood estimator are considered. Our aim is to estimate the unknown parameters for stochastic differential equation with discrete time observation data. In simulation study we compare the non-parametric method with maximum likelihood method using stochastic numerical scheme named with Euler Maruyama.

Hybrid Genetic Algorithm: A Robust Parameter Estimation Technique and Its Application to Heavy Duty Vehicles

2003 ◽  
Author(s):  
Jie Xiao ◽  
Bohdan Kulakowski
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Hybrid Genetic Algorithm ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Optimization Techniques ◽  
Estimation Technique ◽  
Estimation Strategy ◽  
Analysis Experiment

This study aims at establishing an accurate yet efficient parameter estimation strategy for developing dynamic vehicle models that can be easily implemented for simulation and controller design purposes. Generally, conventional techniques such as Least Square Estimation (LSE), Maximum Likelihood Estimation (MLE), and Instrumental Variable Methods (IVM), can deliver sufficient estimation results for given models that are linear-in-the-parameter. However, many identification problems in the engineering world are very complex in nature and are quite difficult to solve by those techniques. For the nonlinear-in-the-parameter models, it is almost impossible to find an analytical solution. As a result, numerical algorithms have to be used in calculating the estimates. In the area of model parameter estimation for motor vehicles, most studies performed so far have been limited either to the linear-in-the-parameter models, or in their ability to handle multi-modal error surfaces. For models with nondifferentiable cost functions, the conventional methods will not be able to locate the optimal estimates of the unknown parameters. This concern naturally leads to the exploration of other search techniques. In particular, Genetic Algorithms (GAs), as population-based global optimization techniques that emulate natural genetic operators, have been introduced into the field of parameter estimation. In this paper, hybrid parameter estimation technique is developed to improve computational efficiency and accuracy of pure GA-based estimation. The proposed strategy integrates a GA and the Maximum Likelihood Estimation. Choices of input signals and estimation criterion are discussed involving an extensive sensitivity analysis. Experiment-related aspects, such as imperfection of data acquisition, are also considered. Computer simulation results reveal that the hybrid parameter estimation method proposed in this study shows great potential to outperform conventional techniques and pure GAs in accuracy, efficiency, as well as robustness with respect to the initial guesses and measurement uncertainty. Primary experimental validation is also implemented including interpretation and processing of field test data, as well as analysis of errors associated with aspects of experiment design. To provide more guidelines for implementing the hybrid GA approach, some practical guidelines on application of the proposed parameter estimation strategy are discussed.

Reliability Analysis of a Small Pneumatic Cylinder Life

2011 ◽  
Vol 110-116 ◽  
pp. 4240-4245
Author(s):  
Jun Zhao Zhang ◽  
Cong Ling Wang ◽  
Xue Fa Fang
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Distribution Model ◽  
Pneumatic Cylinder ◽  
Life Test ◽  
Life Distribution ◽  
Median Rank ◽  
Distribution Parameters

The reliability of the pneumatic cylinder was investigated by routine life test. The results show that the failures of the pneumatic cylinder can be described as a Weibull distribution and fatigue fracture of the aluminum end cap and the head of install bolt is the major failure for the pneumatic cylinder. The pneumatic cylinder life distribution parameters were estimated by the median rank method in combination with maximum likelihood method. The distribution model for the reliability of the pneumatic cylinder was also proposed here.

Maximum Likelihood Parameter Estimation of CNC System Reliability

2014 ◽  
Vol 487 ◽  
pp. 282-285
Author(s):  
Yan Gu ◽  
Yi Qiang Wang ◽  
Xiao Qin Zhou ◽  
Xiu Hua Yuan
Keyword(s):  
Genetic Algorithm ◽  
Parameter Estimation ◽  
Maximum Likelihood ◽  
System Reliability ◽  
Simulated Annealing Algorithm ◽  
Likelihood Function ◽  
Estimation Method ◽  
Distribution Model ◽  
Improved Genetic Algorithm ◽  
Cnc System

In order to increase calculation accuracy of CNC system reliability, this paper proposed a maximum likelihood parameter estimation method based on improved genetic algorithm. In the parameter estimation process for CNC system reliability distribution model, the maximum likelihood function value was gained by improving genetic algorithm through simulated annealing algorithm. Parameter estimation was carried out by setting Weibull distribution as an example. The result shows that the improved genetic algorithm can increase solution efficiency and convergence rate. Besides, it can effectively estimate parameters of reliability distribution model.

Sign in / Sign up

Export Citation Format

Share Document