最大熵原理及改进方法的研究现状

熵作为信息论中的一个基本概念受到了广泛的关注与研究.以熵为基础的最大熵原理也在众多学者的研究与应用中不断发展,逐渐形成了自有的理论体系并得到了广泛应用,例如在使用贝叶斯方法进行测量不确定度评定时,最大熵原理可以估计先验分布.本文以Shannon熵为主要对象,对目前研究中涉及的不同约束下最大熵原理进行了归纳,并整理为形式...     

Parameter estimation for bivariate Weibull distribution using generalized moment method for reliability evaluation

Bivariate Weibull distribution can address the life of a system exhibiting 2‐dimensional characteristics in risk and reliability engineering. The applicability of bivariate Weibull distribution has been hindered by its difficulty with parameter estimation, as the number of parameters in bivariate Weibull distribution is more than those in univariate Weibull distribution. Considering a particular structure of a bivariate Weibull distribution model, this paper proposes a generalized moment method (GMM) for parameter estimation. This GMM method is simple, and it has proved to be efficient. The GMM can guarantee the existence and the uniqueness of the solution. A confidence interval for each estimator is derived from the moments of the bivariate distribution. The paper presents a simulation case and 2 real cases to demonstrate the proposed methods.     

非高斯随机过程的短期极值估计:复合Hermite模型

Hermite模型自20世纪80年代后期开始被广泛应用于非高斯随机过程的短期极值估计。当随机过程的非高斯性很强时,尤其是偏度很大时,常用的3阶Hermite模型不足以表征出极值分布的尾端特征。工程中,样本统计矩的不确定性使得更高阶的Hermite模型不宜使用。基于此,该文提出了同时基于中心矩与线性矩的复合Hermite模型,有效地将Hermite模型由3阶拓展到4阶。该文以对数正态模型作为非线性系统的研究对象,对比分析了在解析条件下和在使用蒙特卡洛模拟获得样本数据条件下,各类Hermite模型与传统的Gumbel法以及平均条件穿越率（ACER）法用于极值分析的表现。结果表明,对于大偏度强非高斯随机过程的极值预测,复合Hermite模型具有更好的精确度和鲁棒性。     

Error estimation in a stochastic finite element method in electrokinetics

Input data to a numerical model are not necessarily well known. Uncertainties may exist both in material properties and in the geometry of the device. They can be due, for instance, to ageing or imperfections in the manufacturing process. Input data can be modelled as random variables leading to a stochastic model. In electromagnetism, this leads to solution of a stochastic partial differential equation system. The solution can be approximated by a linear combination of basis functions rising from the tensorial product of the basis functions used to discretize the space (nodal shape function for example) and basis functions used to discretize the random dimension (a polynomial chaos expansion for example). Some methods (SSFEM, collocation) have been proposed in the literature to calculate such approximation. The issue is then how to compare the different approaches in an objective way. One solution is to use an appropriate a posteriori numerical error estimator. In this paper, we present an error estimator based on the constitutive relation error in electrokinetics, which allows the calculation of the distance between an average solution and the unknown exact solution. The method of calculation of the error is detailed in this paper from two solutions that satisfy the two equilibrium equations. In an example, we compare two different approximations (Legendre and Hermite polynomial chaos expansions) for the random dimension using the proposed error estimator. In addition, we show how to choose the appropriate order for the polynomial chaos expansion for the proposed error estimator. Copyright © 2009 John Wiley & Sons, Ltd.     

Confidence interval for the mean of non‐normal data

The problem of constructing a confidence interval for the mean of non‐normal data is considered. The Bootstrap method and the Box–Cox transformation method of constructing the confidence interval are compared with the normal theory method. Simulation studies are used to evaluate the performance of these different methods of constructing confidence intervals. The result is not surprising; the Bootstrap method is more effective and efficient than the Box–Cox transformation method and the normal theory method in this simulation study. A real example demonstrates the ability of these methods to construct a confidence interval for the mean of audit accounting data. Copyright © 2001 John Wiley & Sons, Ltd.     

A seismic optimization procedure for reinforced concrete framed buildings based on eigenfrequency optimization

Several seismic optimization methods have been proposed to improve the performance of reinforced concrete framed (RCF) buildings; however, they have not been widely adopted among practising engineers because they require complex nonlinear models and are computationally expensive. This article presents a procedure to improve the seismic performance of RCF buildings based on eigenfrequency optimization, which is effective, simple to implement and efficient. The method is used to optimize a 10-storey regular building, and its effectiveness is demonstrated by nonlinear time history analyses, which show important reductions in storey drifts and lateral displacements compared to a non-optimized building. A second example for an irregular six-storey building demonstrates that the method provides benefits to a wide range of RCF structures and supports the applicability of the proposed method.     

有色观测噪声背景下正弦信号参量估计的互谱Levinson方法

本文从理论上证明了互相关函数的Yule-Walker方程，并在此基础上提出了互谱AR模型参数估计的Levinson递推自满，该自满可有效地克服传统互谱估计的FFT方法和周期图法存在的谱分辩率低、谱估计方差大等缺点，仿真试验表明，该方法还可有效的克服有色观测噪声对测量精度的影响。     

Performance study of marginal posterior density estimation via Kullback-Leibler divergence

In this article, we introduce Kullback-Leibler (K-L) divergence as a performance measure of marginal posterior density estimation. We show that the K-L divergence can be used to compare two density estimators as well as to assess convergence of a marginal density estimator. We also examine performance of the importance-weighted marginal density estimation (IWMDE) proposed by Chen (1994) under the K-L divergence and we further extend the IWMDE to some more complex Bayesian models where the kernel method, which is widely used for estimating marginal densities using Markov chain Monte Carlo (MCMC) sampling outputs is not applicable. Finally, we use a constrained linear multiple regression model as an example to illustrate our methodology.     

Fault detection and identification in dynamic systems with noisy data and parameter/modeling uncertainties

A probabilistic approach is presented which can be used for the estimation of system parameters and unmonitored state variables towards model-based fault diagnosis in dynamic systems. The method can be used with any type of input–output model and can accommodate noisy data and/or parameter/modeling uncertainties. The methodology is based on Markovian representation of system dynamics in discretized state space. The example system used for the illustration of the methodology focuses on the intake, fueling, combustion and exhaust components of internal combustion engines. The results show that the methodology is capable of estimating the system parameters and tracking the unmonitored dynamic variables within user-specified magnitude intervals (which may reflect noise in the monitored data, random changes in the parameters or modeling uncertainties in general) within data collection time and hence has potential for on-line implementation.     

利用Krawtchouk矩不变量实现基于形状的图像检索

图像在经过平移、旋转和尺度变化后是否仍具有很好的检索效果是基于形状的图像检索研究的一个难点.本文提出了一种利用Krawtchouk矩不变量实现基于形状的图像检索方法.该方法首先对图像进行灰度变换,然后提取图像的低阶矩,取16个低阶矩不变量作为图像的特征向量,并按照相似性度量输出相似图像从而实现基于形状的图像检索.文中给出了实验结果,并与基于几何矩不变量和基于Zernike矩不变量的图像检索方法进行了比较.结果表明本文的方法具有更好的检索性能,和上述两种方法相比,查全率分别提高了21.52%和7.6%,查准率则分别提高了16.25%和6.25%.     

Estimation of relative SD

The relative SD is a measure that is now in common use in the pharmaceutical industry, for example, in pharmaceutical development and analytical chemistry, pharmacology, and quality control. This article comments on the usual point estimate of the true value; presents seven interval estimation methods, easily implemented on a desktop computer; and compares their individual merits and drawbacks. Finally, the question of determining an adequate sample size is addressed, and a possible solution is indicated.     

Estimation of Relative SD

The relative SD is a measure that is now in common use in the pharmaceutical industry, for example, in pharmaceutical development and analytical chemistry, pharmacology, and quality control. This article comments on the usual point estimate of the true value; presents seven interval estimation methods, easily implemented on a desktop computer; and compares their individual merits and drawbacks. Finally, the question of determining an adequate sample size is addressed, and a possible solution is indicated.     

Reliability analysis of Weibull multicomponent system with stress-dependent parameters from accelerated life data

In this paper, reliability estimation of multicomponent system under a multilevel accelerated life testing. When the lifetime of components follows Weibull distribution, the problem of point and interval estimates are discussed from different perspectives. Under a general life-stress assumption that there are multiple nonconstant and stress-dependent scale and shape parameters, the maximum likelihood estimates of unknown parameters along with associated existence and uniqueness are established. Approximate confidence intervals are constructed correspondingly via expected Fisher information matrix. Furthermore, some pivotal quantities are constructed and alternative generalized point and interval estimates are also proposed for comparison. In addition, predictive intervals for the lifetime of the multicomponent system are discussed under classical and generalized pivotal approaches, respectively. The results show that the proposed generalized estimates are superior to the conventional likelihood approach in terms of the accuracy. A real data example is carried out to illustrate the implementations of the proposed methods.     

基于整体-局部弯曲模型的钢-混凝土组合梁界面滑移及其效应分析

提出了具有界面滑移的钢-混凝土组合梁截面弯矩由不考虑滑移的整体梁承担整体弯矩和自由滑移的叠合梁承担局部弯矩的整体-局部弯曲模型。基于Bernoulli梁理论和抗剪连接件线性剪力-滑移模型,建立了截面弯矩及剪力分配的计算方法,得到了整体-局部弯曲模型计算界面滑移及考虑界面滑移的截面应力和梁弯曲挠度的公式,并给出了集中荷载作用下简支组合梁的栓钉剪力及界面滑移计算公式。     

Online parameter estimation and run-to-run process adjustment using categorical observations

Categorical observations are frequently observed in run-to-run processes where obtaining accurate measurements of quality characteristics is difficult. In such circumstances, the use of categorical observations to estimate a process model and generate an adjustment recipe becomes inevitable. However, most conventional run-to-run controllers cannot be applied if no continuous observations are available; some parameter estimation methods that can handle categorical data only use historical dataset in an offline manner. In practice, it is common to see observations collected following a time sequence in a run-to-run process. Taking the lapping process in semiconductor manufacturing as an example, this paper develops an online approach for parameters estimation and run-to-run process adjustment using categorical observations. The proposed method optimises a penalised Maximum Likelihood (ML) function and updates parameters step by step when new categorical observations become available. A control strategy is also derived to generate receipts for process update between runs. The computational results of performance evaluation show that the proposed method is capable of estimating unknown parameters and control output quality online when initial bias exists.     

A fuzzy logic based approach to reliability improvement estimation during product development

During early stages of product development process, a vast amount of knowledge and information is generated. However, most of it is subjective (imprecise) in nature and remains unutilized. This paper presents a formal structure for capturing this information and knowledge and utilizing it in reliability improvement estimation. The information is extracted as improvement indices from various design tools, experiments, and design review records and treated as fuzzy numbers or linguistic variables. Fuzzy reasoning method is used to combine and quantify the subjective information to map their impact on product reliability. The crisp output of the fuzzy reasoning process is treated as new evidence and incorporated into a Bayesian framework to update the reliability estimates. A case example is presented to demonstrate the proposed approach.     

Bayes estimation of residual life by fusing multisource information

Residual life estimation is essential for reliability engineering. Traditional methods may experience difficulties in estimating the residual life of products with high reliability, long life, and small sample. The Bayes model provides a feasible solution and can be a useful tool for fusing multisource information. In this study, a Bayes model is proposed to estimate the residual life of products by fusing expert knowledge, degradation data, and lifetime data. The linear Wiener process is used to model degradation data, whereas lifetime data are described via the inverse Gaussian distribution. Therefore, the joint maximum likelihood (ML) function can be obtained by combining lifetime and degradation data. Expert knowledge is used according to the maximum entropy method to determine the prior distributions of parameters, thereby making this work different from existing studies that use non-informative prior. The discussion and analysis of different types of expert knowledge also distinguish our research from others. Expert knowledge can be classified into three categories according to practical engineering. Methods for determining prior distribution by using the aforementioned three types of data are presented. The Markov chain Monte Carlo is applied to obtain samples of the parameters and to estimate the residual life of products due to the complexity of the joint ML function and the posterior distribution of parameters. Finally, a numerical example is presented. The effectiveness and practicability of the proposed method are validated by comparing it with residual life estimation that uses non-informative prior. Then, its accuracy and correctness are proven via simulation experiments.     

On the upper truncated Weibull distribution and its reliability implications

The characteristics and application of the truncated Weibull distribution are studied in this paper. This distribution is applicable to the situation where the test data are bounded in an interval because of test conditions, cost and other restrictions. An important property of the truncated Weibull distribution is that it can have bathtub-shaped failure rate function. In this paper, the parametric analysis and parameter estimation methods of the distribution are investigated. Both the graphical approach and the maximum likelihood estimation are considered. The applicability of this distribution to modeling lifetime data is illustrated by an example and the results of comparisons to other competitive models in modeling the given data are also presented. Moreover, the possible application of the distribution to modeling component or system failure is discussed.     

Analysis of Field Return Data With Failed-But-Not-Reported Events

Warranty data contain valuable information on product field reliability and customer behaviors. Most previous studies on analysis of warranty data implicitly assume that all failures within the warranty period are reported and recorded. However, the failed-but-not-reported (FBNR) phenomenon is quite common for a product whose price is not very high. Ignorance of the FBNR phenomenon leads to an overestimate of product reliability based on field return data or an overestimate of warranty cost based on lab data or tracking data. Being an indicator of customer satisfaction, the FBNR proportion provides valuable managerial insights. In this study, statistical inference for the FBNR phenomenon as well as field lifetime distribution is described. We first propose a flexible FBNR function to model the time-dependent FBNR behavior. Then, a framework for data analysis is developed. In the framework, both semiparametric and parametric approaches are used to jointly analyze warranty claim data and supplementary tracking data from a follow-up of selected customers. The FBNR problem in the tracking data is minimal and thus the data can be used to effectively decouple the FBNR information from the warranty claim data. The proposed methods are illustrated with an example. Supplementary materials for this article are available online.     

The Application of Random Balance Designs

In the chemical and petrochemical industries kinetic models are useful for describing the physical and chemical steps that occur in commercial processes. Often kinetic models involve several responses. Box and Draper (1965) have demonstrated that using multiresponse data for estimating the parameters in a model results in confidence regions for the parameters that are smaller than those obtained when the responses are considered individually, and they have developed a procedure for the multiresponse estimation of common parameters. Using multiresponse data also provides a better understanding of the reaction mechanism and makes possible a more comprehensive assessment of the correctness of the proposed model. Data from an oil shale pyrolysis experiment was used to fit and critique a sequence of models. These showed that conversion of the organic material in shale to oil was better explained when an intermediate product was included in the reaction network, and multiresponse techniques were employed. This led to a plausible kinetic representation of the pyrolysis process. Multiresponse models for more complex reaction mechanisms may require the estimation of a large number of parameters. An example is given, methods for minimizing computational difficulties in this situation are discussed, and some numerical results are presented.