混合高斯参数估计的两种EM算法比较

混合高斯模型是一种典型的非高斯概率密度模型,获得广泛应用。其参数的优效估计可以通过最大似然方法获得,但最大似然估计往往因其非线性而难以实现,故期望最大化(Expectation-Maximization,EM)迭代算法成为一种常用的替代方法。常规EM算法性能受迭代初值设置影响大,且不能对模型阶数做出估计。一种名为贪婪EM的改进算法可以克服这两个缺点,获得更为准确的模型参数估计,但其运算量一般会远大于前者。本文对这两种EM算法进行综合研究,深入挖掘两者之间的关系,并基于相同的数值仿真实例,直观地演示比较两者的性能差异。     

基于EM算法和模态形式的状态空间模型自降阶工作模态分析

工作模态分析具有试验简单、经济可行等优点,在工程实际中有广泛的应用。在基于状态空间模型的模态分析中,模型阶次的确定是获得准确和稳定的模态参数的关键问题之一。该文结合期望最大(EM)算法和模态形式状态空间模型来实现模型自降阶和模态参数估计。将状态空间模型变换到模态形式,使待估计参数量得到精简的同时,可直接估计各阶模态响应。引入表征各阶模态响应在实际响应中占比的模态贡献作为模型降阶的指标,在EM求解模型极大似然估计时实现模型降阶。同时结合频谱图分析和阻尼比阈值剔除虚假模态,以获得实际的结构模态信息。通过数值结构模拟和现场结构实测的数据分析,结果表明该文方法具有较好的适用性和有效性。     

非理想信道估计条件下OFDM系统的最大似然检测算法

基于最大似然的准则,研究了理想信道估计条件下和非理想信道估条件下OFDM系统的最优检测算法。研究结果表明,当发送信号为PSK调制方式时,无论是理想信道估计还是非理想信道估计,最大似然检测算法与传统的迫零检测算法等价。但当信道估计非理想且发送信号的调制方式为16QAM或高阶QAM时,采用最大似然检测算法才能够获得更好的性能。     

最大似然阵处理的迭代算法

本文提出了在最大似然阵处理中以矢量的内积运算代替交错投影法的二次项运算的迭代算法。这种算法减小了运算量,收敛、性能好。计算机模拟结果验证了算法的有效性。     

数字采样测量噪声误差的估计和分析

针对高频数字采样中的附加噪声和时间抖动误差估计问题，给出了高频数字采样测量噪声误差的最大似然估计方法。在获得了相应的数学模型后，对最小二乘估计和最大似然估计方法进行了比较。仿真结果表明，对于此类误差最大似然估计比最小二乘估计有效性更好。另外最大似然估计的一个优点是用于不确定度计算的克拉美一罗下限值更易于获得。     

用多项式模型和自适应滤波估计瞬时频率

本文论述了非平稳信号瞬时频率(IF)的估计方法,包括基干最小均方误差(LMS)算法或递推最小二乘(RLS)算法的自适应IF估计方法和基于信号相位多项式模型的IF估计方法。对各种估计方法的估计方差与理论方差下限进行了比较。说明了,基于互Wigner分布的估计方法所需信噪比(SNR)门限值最低。在低SNR、短信号记录的情况下,用多项式相位模型与最大似然法可以获得比较可靠的IF估计。     

基于最大似然估计的辐射噪声源近场定位方法性能分析

如何利用较少的阵元个数得到比较理想的空间分辨力,准确找到噪声源位置,一直是人们比较关心的问题,因此介绍了基于最大似然估计的辐射噪声源近场定位方法,并利用遗传算法寻求最大似然估计的全局最优解,从而实现噪声源近场定位,其具有比常规聚焦波束形成更高的空间分辨力,且可以有效实现相干声源近场定位。通过计算机仿真详细分析了信噪比、测量距离及基阵孔径对本文算法定位性能的影响,说明了仅利用小孔径基阵就可实现辐射噪声源近场高分辨定位,最后通过湖试实验验证了该方法的有效性,具有一定的工程应用价值。     

基于修正EM的高效MIMO-OFDM系统MAP信道估计算法

针对MIMO-OFDM系统的基于期望最大化(EM)的最大后验(MAP)信道估计算法带来的误差地板(EF)现象及较低的数据传输效率,提出了一种基于修正EM的高效的MAP信道估计算法.该算法首先引入一种更精确的系统模型来改善基于EM的MAP估计算法在高信噪比下的EF现象,其次利用多个正交频分复用(OFDM)符号进行联合信道...     

基于贝叶斯信息融合的测量不确定度评定与实时更新

基于贝叶斯信息融合与统计推断原理,建立不确定度动态评定模型,对测量不确定度进行实时更新。引入最大熵原理和爬山搜索优化算法,确定先验分布概率密度函数及样本信息似然函数,结合贝叶斯公式求出后验分布概率密度函数,实现不确定度的优化估计。仿真及实例分析表明,基于贝叶斯和最大熵方法评定及更新的测量不确定度更加接近理论值。     

Chirp信号参数估计算法性能比较

通过数值仿真定量地比较了三种Chirp信号参数估计算法——解线调法、迭代估计法和局部搜索最大似然法的性能，并定性地比较了算法的运算量。仿真结果表明，在三种算法中，局部搜索最大似然法的估计性能最好，而运算量居中；解线调法运算量最大，但估计性能居中；迭代估计法的估计性能最差，但运算量最小。对于实际系统，应根据不同的估计精度和运算量要求，灵活选择不同的算法。综合考虑估计性能和运算量之间的折衷可以得到结论，在三种算法中局部搜索最大似然法是一种相对较好的选择。     

Change‐Point Detection for Shifts in Control Charts Using EM Change‐Point Algorithms

Knowing the time of changes in mean and variance in a process is crucial for engineers to identify the special cause quickly and correctly. Because assignable causes may give rise to changes in mean and variance at the same time, monitoring the mean and variance simultaneously is required. In this paper, a mixture likelihood approach is proposed to detect shifts in mean and variance simultaneously in a normal process. We first transfer the change point model formulation into a mixture model and then employ the expectation and maximization algorithm to estimate the time of shifts in mean and variance simultaneously. The proposed method called EMCP (expectation and maximization change point) can be used in both phase I and II applications without the knowledge of in‐control process parameters. Moreover, EMCP can detect the time of multiple shifts and simultaneously produce the estimates of shifts in each individual segment. Numerical data and real datasets are employed to compare EMCP with the direct statistical maximum likelihood method without the use of mixture models. The experimental results show the superiority and effectiveness of the proposed EMCP. The outperformance of EMCP in detecting the time of small shifts is particularly important and beneficial for engineers to identify assignable causes rapidly and accurately in phase II applications in which small shifts occur more often and hence lead to a large average run length. Copyright © 2015 John Wiley & Sons, Ltd.     

EM algorithm for estimating the Burr XII parameters with multiple censored data

The two‐parameter Burr XII distribution has been widely used in various practical applications such as business, chemical engineering, quality control, medical research and reliability engineering. In this paper, we present maximum likelihood estimation (MLE) via the expectation–maximization (EM) algorithm to estimate the Burr XII parameters with multiple censored data. We also provide a method that can be used to construct the confidence intervals of the parameters, a method that computes the asymptotic variance and the covariance of the MLE from the complete and missing information matrices. A simulation study is conducted to compare the performance of the MLE via the EM algorithm and the Netwon–Raphson (NR) algorithm. The simulation results show that the EM algorithm outperforms the NR algorithm in most cases in terms of bias and errors in the root mean square. A numerical example is also used to demonstrate the performance of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

Field data analyses with additional after-warranty failure data

This paper proposes methods of estimating the lifetime distribution for situations where additional field data can be gathered after the warranty expires in a parametric time to failure distribution. For satisfactory inference about parameters involved, it is desirable to incorporate these after-warranty data in the analysis. It is assumed that after-warranty data are reported with probability p₁(<1), while within-warranty data are reported with probability 1. Methods of obtaining maximum likelihood estimators are outlined, their asymptotic properties are studied, and specific formulas for Weibull distribution are obtained. An estimation procedure using the expectation and maximization algorithm is also proposed when the reporting probability is unknown. Simulation studies are performed to investigate the properties of the estimates.     

Filtered backprojection algorithm can outperform iterative maximum likelihood expectation‐maximization algorithm

The iterative maximum‐likelihood expectation‐maximization (ML‐EM) algorithm is an excellent algorithm for image reconstruction and usually provides better images than the filtered backprojection (FBP) algorithm. However, a windowed FBP algorithm can outperform the ML‐EM in certain occasions, when the least‐squared difference from the true image, that is, the least‐squared error (LSE), is used as the comparison criterion. Computer simulations were carried out for the two algorithms. For a given data set the best reconstruction (compared to the true image) from each algorithm was first obtained, and the two reconstructions are compared. The stopping iteration number of the ML‐EM algorithm and the parameters of the windowed FBP algorithm were determined, so that they produced an image that was closest to the true image. However, to use the LSE criterion to compare algorithms, one must know the true image. How to select the optimal parameters when the true image is unknown is a practical open problem. For noisy Poisson projections, computer simulation results indicate that the ML‐EM images are better than the regular FBP images, and the windowed FBP algorithm images are better than the ML‐EM images. For the noiseless projections, the FBP algorithms outperform the ML‐EM algorithm. The computer simulations reveal that the windowed FBP algorithm can provide a reconstruction that is closer to the true image than the ML‐EM algorithm. © 2012 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 22, 114–120, 2012     

Parameter estimation for load‐sharing system subject to Wiener degradation process using the expectation‐maximization algorithm

In practice, many systems exhibit load‐sharing behavior, where the surviving components share the total load imposed on the system. Different from general systems, the components of load‐sharing systems are interdependent in nature, in such a way that when one component fails, the system load has to be shared by the remaining components, which increases the failure rate or degradation rate of the remaining components. Because of the load‐sharing mechanism among components, parameter estimation and reliability assessment are usually complicated for load‐sharing systems. Although load‐sharing systems with components subject to sudden failures have been intensely studied in literatures with detailed estimation and analysis approaches, those with components subject to degradation are rarely investigated. In this paper, we propose the parameter estimation method for load‐sharing systems subject to continuous degradation with a constant load. Likelihood function based on the degradation data of components is established as a first step. The maximum likelihood estimators for unknown parameters are deduced and obtained via expectation‐maximization (EM) algorithm considering the nonclosed form of the likelihood function. Numerical examples are used to illustrate the effectiveness of the proposed method.     

基于比例型Paris公式和逆高斯过程的金属疲劳裂纹扩展随机模型

疲劳失效是金属构件的主要失效方式之一,该文针对金属疲劳裂纹扩展过程中的不确定性,以“首次达到给定裂纹长度a的时间t(a)”为随机描述量,采用比例型Paris公式描述裂纹的平均扩展路径,建立基于逆高斯过程的单样本疲劳裂纹扩展随机模型和考虑样本异质性的裂纹扩展随机效应模型,分别采用最大似然估计法(MLE)和最大期望算法(EM)推导了单样本模型和随机效应模型的参数估计公式。最后,利用提出的裂纹扩展随机模型拟合了68个铝合金板的疲劳裂纹数据,对结果进行了拟合优度分析。结果表明:该文提出的疲劳裂纹扩展随机模型能够有效地分析和解释金属疲劳裂纹扩展过程中的不确定性。     

Maximum Likelihood Estimation for a Hidden Semi‐Markov Model with Multivariate Observations

In this paper, a parameter estimation procedure for a condition‐based maintenance model under partial observations is presented. The deterioration process of the partially observable system is modeled as a continuous‐time homogeneous semi‐Markov process. The system can be in a healthy or unhealthy operational state, or in a failure state, and the sojourn time in the operational state follows a phase‐type distribution. Only the failure state is observable, whereas operational states are unobservable. Vector observations that are stochastically related to the system state are collected at equidistant sampling times. The objective is to determine maximum likelihood estimates of the model parameters using the Expectation–Maximization (EM) algorithm. We derive explicit formulae for both the pseudo likelihood function and the parameter updates in each iteration of the EM algorithm. A numerical example is developed to illustrate the efficiency of the estimation procedure. Copyright © 2012 John Wiley & Sons, Ltd.     

Field reliability modeling based on two-dimensional warranty data with censoring times

ABSTRACT

Warranty data can be used for estimating product reliability, identifying causes of failure and designing warranty policy. Based on two-dimensional warranty data, we utilize an accelerated failure time model to investigate the effect of usage rate on product degradation. The stochastic expectation-maximization algorithm is proposed to estimate parameters of the reliability model considering both censored data and field data. Extensive simulation studies are used to validate the proposed method and to compare it with the maximum likelihood method. The utilities of the results have been demonstrated through real warranty data collected from an automobile manufacturer in China.