基于蜂群算法的等压灌装阀阀口流道结构优化

目的为了改善等压灌装阀的灌装性能,分析阀口流道结构参数对液料流场的影响,求解流道内最大压力损失、最大液料流速和最大湍动能均最小化的约束多目标优化问题。方法基于正交试验设计和Fluent流场仿真软件对灌装阀阀口流道流场进行数值模拟,并通过回归分析建立以阀口流道结构参数为自变量的最大压力损失、最大液料流速和最大湍动能的经验方程,进而建立阀口流道结构参数约束多目标优化模型,采用约束多目标人工蜂群算法对优化模型进行求解。结果流道内最大压力损失最小化、最大液料流速最小化和最大湍动能最小化这3个目标之间存在冲突,无法同时达到最优,基于多目标人工蜂群算法获得了阀口流道结构参数的最优Pareto解集。结论约束多目标人工蜂群算法能有效用于等压灌装阀阀口流道结构参数的优化。     

Reliability analysis for wind turbines with incomplete failure data collected from after the date of initial installation

Reliability has an impact on wind energy project costs and benefits. Both life test data and field failure data can be used for reliability analysis. In wind energy industry, wind farm operators have greater interest in recording wind turbine operating data. However, field failure data may be tainted or incomplete, and therefore it needs a more general mathematical model and algorithms to solve the model. The aim of this paper is to provide a solution to this problem. A three-parameter Weibull failure rate function is discussed for wind turbines and the parameters are estimated by maximum likelihood and least squares. Two populations of German and Danish wind turbines are analyzed. The traditional Weibull failure rate function is also employed for comparison. Analysis shows that the three-parameter Weibull function can obtain more accuracy on reliability growth of wind turbines. This work will be helpful in the understanding of the reliability growth of wind energy systems as wind energy technologies evolving. The proposed three-parameter Weibull function is also applicable to the life test of the components that have been used for a period of time, not only in wind energy but also in other industries.     

基于GM-噪声SVR方法的矿山设备可靠性参数估计

为了有效估计小子样条件下矿山设备的三参数威布尔分布可靠性模型参数,提出基于GM-噪声SVR的参数估计方法。该方法以灰色估计法(GM)为基础估计模型的位置参数,采用基于训练样本数量和噪声参数寻优的ε - 带支持向量回归机(ε-SVR)估计尺度参数和形状参数,并通过拟合的三参数威布尔分布函数分析预测和解决设备的可靠性问题。算例结果表明,GM-噪声SVR方法可以很好地用于矿山设备可靠性模型参数估计,估计某带式输送机三参数威布尔分布可靠性模型的位置参数、尺度参数和形状参数依次为3.1525、188.3763、1.0476,平均无故障时间为188 h,标准均方根误差NRMSE为0.0519。这表明该方法的可行性和有效性。     

A Method for Discriminating Between Failure Density Functions Used In Reliability Predictions

Unless sufficient evidence to the contrary exists, the exponential distribution is often assumed as a model for the failure density function in reliability predictions.

The generalized gamma distribution, with known location parameter, is a three parameter distribution which encompasses the exponential, Weibull, gamma and many others. In this paper, (i) maximum likelihood estimation for the three parameters is indicated, (ii) it is noted that these estimators are asymptotically multivariate normally distributed, and (iii) using the distribution of the estimators, probability regions for the estimators of the parameters of the generalized gamma distribution are established for large sample situations.

In situations where the generalized gamma can be assumed as the correct density function, the exponential and the Weibull are special cases. A method is presented using experimental or life data for rejecting (with a known probability of false rejection) the Weibull and (or) the exponential functions when they do not appear to describe the failure density function of a unit.     

Statistical Inference From Censored Weihull Samples

In life testing experiments it is a fairly common practice to terminate the experiment before all items have failed. The Weibull distribution is often used as a model for the observations and when a computer is available maximum likelihood estimation of the parameters is to be recommended. The tables presented in this paper enable one to set confidence limits on the parameters and the reliability based on the maximum likelihood estimates for selected censoring and sample sizes.

It is also observed that, as in the case with no censoring, the maximum likelihood estimator of the reliability is very nearly unbiased and its variance is near the Cramér-Rao lower bound, Unbiasing factors for the maximum likelihood estimator of the shape parameter are given.     

Estimation of mixed Weibull distribution parameters using the SCEM-UA algorithm: Application and comparison with MLE in automotive reliability analysis

The shuffled complex-evolution metropolis algorithm (SCEM-UA) is used to estimate mixed Weibull distribution parameters in automotive reliability analysis. The results are compared with maximum likelihood estimation (MLE) results. The comparison shows that, in the examples given, SCEM-UA can deliver more accurate results than MLE overall.     

Mathematical Theory of Probability and Statistics

Two test statistics are suggested for discriminating between the exponential model and the more general Weibull or gamma models, and these are compared to some previously used test statistics by Monte Carlo methods. The results of estimating reliability under an exponential assumption when the true model is Weibull is also investigated. These results as well as the tests mentioned above indicate that the exponential model is often not adequate when the more general models hold. In contrast to this result it was found that the Weibull model was quite robust relative to the generalized gamma distribution with regard to reliability estimation. Some general pivotal function properties are presented for the maximum likelihood estimator of reliability for the generalized gamma distribution and similar results also hold for the Weibull procedure under a generalized gamma assumption. These results made a Monte Carlo study of this problem feasible. Since the maximum likelihood estimators are apparently ill-behaved for smaller sample sizes and since the Weibull model is robust it appears little is gained by using the generalized gamma distribution for samples of size less than 200 to 400.     

Lower Percentile Estimation of Accelerated Life Tests with Nonconstant Scale Parameter

Lower percentiles of product lifetime are useful for engineers to understand product failure, and avoiding costly product failure claims. This paper proposes a percentile re‐parameterization model to help reliability engineers obtain a better lower percentile estimation of accelerated life tests under Weibull distribution. A log transformation is made with the Weibull distribution to a smallest extreme value distribution. The location parameter of the smallest extreme value distribution is re‐parameterized by a particular 100pth percentile, and the scale parameter is assumed to be nonconstant. Maximum likelihood estimates of the model parameters are derived. The confidence intervals of the percentiles are constructed based on the parametric and nonparametric bootstrap method. An illustrative example and a simulation study are presented to show the appropriateness of the method. The simulation results show that the re‐parameterization model performs better compared with the traditional model in the estimation of lower percentiles, in terms of Relative Bias and Relative Root Mean Squared Error. Copyright © 2017 John Wiley & Sons, Ltd.     

The mean time between failures for an LCD panel

The calculation of mean time between failures is very important in reliability life data analysis. For different distributions, the values of mean time between failures are always different. The two‐parameter Weibull distribution is widely used in reliability engineering. However, some distributions may offer a better fit of data. This paper aims to develop an algorithm for determining the best‐fitted distribution of a liquid crystal display panel based on the field return data. The two‐parameter and three‐parameter Weibull distributions and other distributions such as the Burr XII distribution, the Pareto distribution and the Log‐logistic distribution are compared to provide a better characterization of the life data which is based on the maximum value of all log‐likelihood functions. We also provide a goodness‐of‐fit test for the best‐fitted distribution. It is recommended that the Burr XII distribution could be used to characterize the reliability life of a liquid crystal display panel. Copyright © 2010 John Wiley & Sons, Ltd.     

Maximum likelihood Estimation of Parameters in the Inverse Gaussian Distribution,With Unknown Origin

Maximum likelihood estimation is applied to the three-parameter Inverse Gaussian distribution, which includes an unknown shifted origin parameter. It is well known that for similar distributions in which the origin is unknown, such as the lognormal, gamma, and Weibull distributions, maximum likelihood estimation can break down. In these latter cases, the likelihood function is unbounded and this leads to inconsistent estimators or estimators not asymptotically normal. It is shown that in the case of the Inverse Gaussian distribution this difticulty does not arise. The likelihood remains bounded and maximum likelihood estimation yields a consistent estimator with the usual asymptotic normality properties. A simple iterative method is suggested for the estimation procedure. Numerical examples are given in which the estimates in the Inverse Gaussian model are compared with those of the lognormal and Weibull distributions.     

Bayesian estimation of the 3-parameter inverse gaussian distribution

The three-parameter inverse Gaussian distribution is used as an alternative model for the three parameter lognormal, gamma and Weibull distributions for reliability problems. In this paper Bayes estimates of the parameters and reliability function of a three parameter inverse Gaussian distribution are obtained. Posterior variance estimates are compared with the variance of their maximum likelihood counterparts. Numerical examples are given.     

A flexible Weibull extension

We propose a new two-parameter ageing distribution which is a generalization of the Weibull and study its properties. It has a simple failure rate (hazard rate) function. With appropriate choice of parameter values, it is able to model various ageing classes of life distributions including IFR, IFRA and modified bathtub (MBT). The ranges of the two parameters are clearly demarcated to separate these classes. It thus provides an alternative to many existing life distributions. Details of parameter estimation are provided through a Weibull-type probability plot and maximum likelihood. We also derive explicit formulas for the turning points of the failure rate function in terms of its parameters. This, combined with the parameter estimation procedures, will allow empirical estimation of the turning points for real data sets, which provides useful information for reliability policies.     

Estimation of weibull reliability from few life tests

The 2–parameter Weibull model can be re–parameterized in terms of shape parameter and a prefixed age for which a reliability estimation is required. Using the uniform and beta priors, some new point and lower bound reliability estimators were derived. These estimators appear to be very suitable to meet the needs of fast and cheap reliability evaluation during production. Their characteristics were studied by means of a Monte Carlo simulation and were compared with those of the maximum likelihood estimators.     

双参数Rayleigh分布环境因子的经验Bayes估计及应用

本文针对Rayleigh分布位置参数已知的情形,给出了Rayleigh分布环境因子的极大似然估计和经验Bayes估计,并将环境因子的估计结果应用于Rayleigh部件的可靠性评估,给出了该部件可靠度函数与失效率的估计。最后的随机模拟例子表明,经验Bayes估计优于极大似然估计,并且在考虑环境因子的情形下,Rayleigh部件可靠性指标的估计优于未考虑环境因子时的估计。     

Robust Regression using Probability Plots for Estimating the Weibull Shape Parameter

The Weibull shape parameter is important in reliability estimation as it characterizes the ageing property of the system. Hence, this parameter has to be estimated accurately. This paper presents a study of the efficiency of using robust regression methods over the ordinary least‐squares regression method based on a Weibull probability plot. The emphasis is on the estimation of the shape parameter of the two‐parameter Weibull distribution. Both the case of small data sets with outliers and the case of data sets with multiple‐censoring are considered. Maximum‐likelihood estimation is also compared with linear regression methods. Simulation results show that robust regression is an effective method in reducing bias and it performs well in most cases. Copyright © 2006 John Wiley & Sons, Ltd.     

Estimating system reliability with fully masked data under Brown-Proschan imperfect repair model

This article presents a statistical procedure for estimating the lifetime distribution of a repairable system based on consecutive inter-failure times of the system. The system under consideration is subject to the Brown-Proschan imperfect repair model. The model postulates that at failure the system is repaired to a condition as good as new with probability p, and is otherwise repaired to its condition just prior to failure. The estimation procedure is developed in a parametric framework for incomplete set of data where the repair modes are not recorded. The expectation-maximization principle is employed to handle the incomplete data problem. Under the assumption that the lifetime distribution belongs to the two-parameter Weibull family, we develop a specific algorithm for finding the maximum likelihood estimates of the reliability parameters, the probability of perfect repair (p), as well as the Weibull shape and scale parameters (α, β) The proposed algorithm is applicable to other parametric lifetime distributions with aging property and explicit form of the survival function, by just modifying the maximization step. We derive some lemmas which are essential to the estimation procedure. The lemmas characterize the dependency among consecutive lifetimes. A Monte Carlo study is also performed to show the consistency and good properties of the estimates. Since useful research is available regarding optimal maintenance policies based on the Brown-Proschan model, the estimation results will provide realistic solutions for maintaining real systems.     

飞机可靠性分析中的混合威布尔分布参数估计方法

为更真实地描述飞机系统的失效规律,提高可靠性分析的准确性,利用混合威布尔分布建立了飞机可靠性分析模型.针对所建立的模型中参数估计困难的问题,基于K-S检验思想,以拟合优度最好为优化目标,将参数估计转化为无约束优化模型,建立了混合威布尔分布参数估计方法.将改进粒子群算法用于优化模型的求解,利用粒子群的适应度方差自动调整加速度因子,提高了优化求解效率并降低了陷入局部最优的概率.计算实例表明,该方法的参数估计精度高于其他方法,而且算法简单、易于实现,收敛速度较快,不易陷入局部最优解.     

Different Estimation Methods for Constant Stress Accelerated Life Test under the Family of the Exponentiated Distributions

The Accelerated Life Testing (ALT) has been used for a long time in several fields to obtain information on the reliability of product components and materials under operating conditions in a much shorter time. One of the main purposes of applying ALT is to estimate the failure time functions and reliability performance under normal conditions. This paper concentrates on the estimation procedures under ALT and how to select the best estimation method that gives accurate estimates for the reliability function. For this purpose, different estimation methods are used, such as maximum likelihood, least squares (LS), weighted LS, and probability weighted moment. Moreover, the reliability function under usual conditions is predicted. The estimation procedures are applied under the family of the exponentiated distributions in general, and for the exponentiated inverted Weibull (EIW) as a special case. Numerical analysis including simulated data and a real life data set is conducted to compare the performances between these four methods. It is found that the ML method gives the best results among other estimation methods. Finally, a comparison between the EIW and the Inverted Weibull (IW) distributions based on a real life data set is made using a likelihood ratio test. It is observed that the EIW distribution can provide better fitting than the IW in case of ALT. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust Estimation for Weibull Distribution in Partially Accelerated Life Tests with Early Failures

Maximum likelihood estimation (MLE) is a frequently used method for estimating distribution parameters in constant stress partially accelerated life tests (CS‐PALTs). However, using the MLE to estimate the parameters for a Weibull distribution may be problematic in CS‐PALTs. First, the equation for the shape parameter estimator derived from the log‐likelihood function is difficult to solve for the occurrence of nonlinear equations. Second, the sample size is typically not large in life tests. The MLE, a typical large‐sample inference method, may be unsuitable. Test items unsuitable for stress conditions may become early failures, which have extremely short lifetimes. The early failures may cause parameter estimate bias. For addressing early failures in the Weibull distribution in CS‐PALTs, we propose an M‐estimation method based on a Weibull Probability Plot (WPP) framework, which leads a closed‐form expression for the shape parameter estimator. We conducted a simulation study to compare the M‐estimation method with the MLE method. The results show that, with early‐failure samples, the M‐estimation method performs better than the MLE does. Copyright © 2015 John Wiley & Sons, Ltd.     

自适应人工蜂群优化极限学习机在拉曼光谱血液定量分析中的应用

提出了一种基于自适应差分进化人工蜂群优化极限学习机预测血液各组分浓度的方法。首先应用人工蜂群算法对输入权值和隐含层阈值迭代寻优;其次结合差分进化进一步提高模型精度且避免后期易陷入局部最优等问题;由于差分进化算法交叉率和变异率存在凭经验给定的不确定性,最后引入了自适应调整的思想提出自适应差分进化人工蜂群算法优化极限学习机算法的模型,将其应用于血液成分定量分析中。实验表明,自适应差分进化人工蜂群算法优化的极限学习机模型具有较高的预测精度,模型具有较强的稳健性。