非线性极大似然法及其在飞机参数辨识中的应用

本文介绍一种非线性极大似然辩识方法。该法以一般非线性动态系统为对象,从系统的非线性模型出发,按极大似然估计准则,经过拟线性化处理建立一个迭代的优化算法。将其应用于某高速飞机气动参数辩识,采用纵横向耦合的六自由度非线性运动方程和非线性气动模型作为飞机数学模型,由飞行试验数据同时估计飞机纵横向稳定性与操纵性导数。计算结果证实,这种算法处理非线性系统是有效的。     

EM算法在统计自然语言处理中的应用

在统计自然语言处理中会经常遇到一类参数估值问题,就是当观察数据为不完全数据时如何求解参数的最大似然估计,EM算法就是解决这类问题的经典算法.给出了EM算法的基本框架,结合HMM和PCFG模型给出如何应用EM算法求解参数的极大似然估计,讨论了EM算法的优点和不足之处.     

LTI状态空间模型的参数估计

采用3种方法研究了LTI(Linear time-invariant)状态空间模型中未知参数的估计问题:利用Metropolis-Hastings算法,从后验分布中抽取一定容量的样本,得出其均值和标准差;采用进化算法来最小化对数似然函数,得到全局最优解;采用模拟退火算法来最大化似然函数,得到全局最优解.最后,通过数值实验验证和比较了3种估计算法的有效性.     

基于极大似然法的椒盐噪声滤波算法

本文提出了一种新的基于极大似然法的椒盐噪声滤波算法。在传统BP算法中引入了极大似然估计,在训练样本时能够在考虑网络逼近行为的同时对噪声分布进行估计。而且针对椒盐噪声模型构造了新的鲁棒误差函数,从而使算法本身的抗干扰性增强。实验结果表明了该算法与传统BP算法相比具有更好的滤波性能。     

相关向量机基函数和超参的协同优化

针对传统相关向量机在训练误差、权值矩阵的稀疏性以及对数边缘似然函数零逼近之间存在冲突,提出利用受试者工作特征曲线对相关向量机参数和核函数进行协同优化。依据模型分类准确率确定合适的核函数;引入模型在5%误判率下的分类准确率,对超参边际似然函数进行改进;为保证权值矩阵稀疏最大化,通过边际似然函数阈值选取最佳相关向量组合,运用交叉验证算法以及各交叉模型的ROC曲线,对相关向量机超参进行最优估计。此外,利用车辆横摆角速度对优化模型进行测试,结果表明:所提算法训练耗时略长,但测试时间明显短于传统估计算法,且模型的分类能力得到大幅提升。     

一种半监督机器学习的EM算法改进方法

EM(Expectation Maximization)算法是含有隐变量(latent variable)的概率参数模型最大似然估计、极大后验概率估计最有效的算法,但很容易进入局部最优现象,对此提出基于半监督机器学习机制的EM算法.本文方法是在最大似然函数中加入惩罚最小二乘因子,同时引入非负约束作为先验信息,结合半监督机器学习方法,将EM算法改进转化为最小化求解问题,再采用最大似然方法求解EM模型,有效估计了混合矩阵和高斯混合模型参数,实现EM算法的改进.仿真结果表明,该方法能够很好地解决了EM算法容易局部最优化问题.     

飞机颤振模态参数辨识的频域广义整体最小二乘算法

采用一种适用于噪声环境的广义整体最小二乘算法,准确地辨识飞机的颠振模态参数．该算法结合有理传递函数模型,将带噪系统的辨识问题转化为广义整体最小二乘问题．利用线性的广义奇异值分解求解模型系数,避免了非线性优化的复杂计算．通过迭代法更新加权项,获得了接近于极大似然估计的辨识效果．最后利用试飞试验数据辨识飞机的模态参数,验证了该方法的有效性．     

基于极大似然准则和最大期望算法的自适应UKF 算法

针对噪声先验统计特性未知情况下的非线性系统状态估计问题,提出了基于极大似然准则和 最大期望算法的自适应无迹卡尔曼滤波(Unscented Kalman filter, UKF) 算法.利用极大似然准则构造含有噪声统计特性的对数似然函数,通 过最大期望算法将噪声估计问题转化为对数似然函数数学期望极大化问题,最终得到带次优递 推噪声统计估计器的自适应UKF算法.仿真分析表明,与传统UKF算法相比,提出的自适应UKF算法 有效克服了传统UKF算法在系统噪声统计特性未知情况下滤波精度下降的问题,并实现了系统噪 声统计特性的在线估计.     

极大似然估计的递推计算灵敏度算法

极大似然估计的递推计算灵敏度算法崔平远，吴瑶华，黄文虎，李乃宏（哈尔滨工业大学航天工程与力学系１５０００１）关键词连续－离散系统，极大似然估计，灵敏度，正交试验玉引言采用极大似然法对连续一离散系统进行参数估计，实际上是一个似然函数的优化计算问题，而其...     

基于增量式有限混合模型的多目标状态极大似然估计

提出了增量式有限混合模型来提取概率假设密度滤波器序贯蒙特卡罗实现方式中的多目标状态. 该模型以增量方式构建, 其混合分量采用逐个方式插入其中. 采用极大似然准则来估计多目标状态. 对于给定分量数目的混合模型, 应用期望极大化算法来获得参数的极大似然解. 在新分量插入混合模型时, 保持已有混合模型的参数不变, 仍旧采用极大似然准则从候选新分量集合中选择新插入分量. 新分量插入混合步和期望极大化算法拟合混合参数步交替应用直到混合分量数目达到概率假设密度滤波器的目标数目估计值. 利用k-d树生成插入到混合模型的新分量候选集合. 增量式有限混合模型统一了分量数目变化趋势和粒子集合似然函数的变化趋势, 有助于一步一步地搜寻混合模型的极大似然解. 仿真结果表明, 基于增量式有限混合模型的概率假设密度滤波器状态提取算法在多目标跟踪的应用中优于已有的状态提取算法.     

GSA-based maximum likelihood estimation for threshold vector error correction model

The log-likelihood function of threshold vector error correction models is neither differentiable, nor smooth with respect to some parameters. Therefore, it is very difficult to implement maximum likelihood estimation (MLE) of the model. A new estimation method, which is based on a hybrid algorithm and MLE, is proposed to resolve this problem. The hybrid algorithm, referred to as genetic-simulated annealing, not only inherits aspects of genetic-algorithms (GAs), but also avoids premature convergence by incorporating elements of simulated annealing (SA). Simulation experiments demonstrate that the proposed method allows to estimate the parameters of larger cointegrating systems. Additionally, numerical results show that the hybrid algorithm does a better job than either SA or GA alone.     

马尔可夫协整回归模型的动态滤波估计

本文提出动态滤波估计方法估计马尔可夫协整回归模型的参数.利用领先和滞后方法构造辅助的动态回归模型,以消除解释变量和误差序列间的相关性以及误差自相关性对估计结果的影响.在Hamilton滤波基础上,应用极大似然方法估计辅助模型的参数.模拟计算结果表明动态滤波估计方法能降低误差序列相关性造成的估计偏差.对1990年1月至2011年10月的中国进出口贸易数据,利用所提方法建立了马尔可夫协整回归模型.     

An innovative approach for modeling of hysteretic energy demand in steel moment resisting frames

This paper presents a new nonlinear model for the prediction of hysteretic energy demand in steel moment resisting frames using an innovative genetic-based simulated annealing method called GSA. The hysteretic energy demand was formulated in terms of several effective parameters such as earthquake intensity, number of stories, soil type, period, strength index, and energy imparted to the structure. The performance and validity of the model were further tested using several criteria. The proposed model provides very high correlation coefficient (R = 0.985), and low root mean absolute error (RMSE = 1,346.1) and mean squared error (MAE = 1,037.6) values. The obtained results indicate that GSA is an effective method for the estimation of the hysteretic energy. The proposed GSA-based model is valuable for routine design practice. The prediction performance of the optimal GSA model was found to be better than that of the existing models.     

基于改进模拟退火算法的软件可靠性模型参数估计方法

为提升现有软件可靠性模型的拟合性能和求解精度,结合软件可靠性模型求解特征,提出一种改进的模拟退火算法。在此基础上,提出基于改进模拟退火算法的软件可靠性模型参数求解方法(简称为MSAE法),并将新方法应用于4组失效数据集。工程应用结果表明,与最大似然估计(MLE)法、和声搜索(HS)算法和蚁群(AC)算法相比,MSAE法可有效改善软件可靠性模型参数求解不收敛的情况,并且可以有效提升现有软件可靠性模型的拟合性能。     

Range,radial velocity,and acceleration MLE using frequency modulation coded LFM pulse train

Linearly frequency modulation (LFM) pulse train and linearly stepped frequency (LSF) pulse train are mostly used in radar systems. However, the estimation performance of target motion parameters may be affected by the high recurrent lobe levels and the range–Doppler coupling phenomenon appearing in ambiguity function (AF). In multi-target scenarios, the estimation performance becomes even worse. The Costas frequency-modulation coded (CFMC) LFM pulse train has an ideal thumbtack-shaped AF, thus it can provide motion parameter estimation with high precision. However, the estimation of target motion parameter for the coherent CFMC LFM pulse train has not been investigated in depth. In this paper, we first analyze the properties of the AF of the CFMC LFM pulse train. Based on its convexity and narrow mainlobe width, a fast method to implement the maximum likelihood estimator (MLE) is proposed to estimate the motion parameters. To reduce the computation complexity, the Chirp-Z Transform (CZT) is introduced. Then, the Cramer–Rao lower bounds (CRLBs) on range, velocity and acceleration for frequency-modulation coded (FMC) pulse train are derived. It is shown that the CRLBs are relevant to the frequency coding patterns. Finally, Monte Carlo simulations are performed to verify the performance of the MLE. The results show that the performance of our proposed method can achieve the CRLBs when the signal-noise ratio (SNR) is higher than the threshold SNR.     

Global sensitivity analysis measures the quality of parameter estimation: The case of soil parameters and a crop model

One common limitation of the use of crop models for decision making in precise crop management is the need for accurate values of soil parameters for a whole field. Estimating these parameters from data observed on the crop, using a crop model, is an interesting possibility. Nevertheless, the quality of the estimation depends on the sensitivity of model output variables to the parameters. The goal of this study is to explain the results for the quality of parameter estimation based on global sensitivity analysis (GSA). The case study consists of estimating the soil parameters by using the STICS-wheat crop model and various synthetic observations on wheat crops (LAI, absorbed nitrogen and grain yield). Suitable criteria summarizing the sensitivity indices of the observed variables were created in order to link GSA indices with the quality of parameter estimation. We illustrate this link on 16 different configurations of different soil, climatic and crop conditions. The GSA indices were computed by the Extended FAST method and a function of RMSE was computed with an importance sampling method based on Bayes theory (GLUE). The proposed GSA-based criteria are able to rank the parameters with respect to their quality of estimation and the different configurations (especially climate and observation set) with respect to their ability to estimate the whole parameter set. They may be used as a tool for predicting the performance of different observation datasets with regard to parameter estimation.     

隐Markov模型参数估计的一种新方法

本文提出一种隐Markov模型参数估计的新方法.该方法直接以模型作识别器时的识别 率最高(或误识率最低)作为估计准则.由该准则导出的算法的性能明显优于最大似然估计 器.文中给出了该算法的一种实现形式. 实验表明,该方法的模型识别率比用最大似然方法求出的模型识别率提高5%左右.     

Alternative Parameter Estimation Methods for the Compound Poisson Software Reliability Model with Clustered Failure Data

The ‘compound Poisson’ (CP) software reliability model was proposed previously by the first named author for time-between-failure data in terms of CPU seconds, using the ‘maximum likelihood estimation’ (MLE) method to estimate unknown parameters; hence, CPMLE. However, another parameter estimation technique is proposed under ‘nonlinear regression analysis’ (NLR) for the compound Poisson reliability model, giving rise to the name CPNLR. It is observed that the CP model, with different parameter estimation methods, produces equally satisfactory or more favourable results as compared to the Musa–Okumoto (M–O) model, particularly in the event of grouped or clustered (clumped) software failure data. The sampling unit may be a week, day or month within which the failures are clumped, as the error recording facilities dictate in a software testing environment. The proposed CPNLR and CPMLE yield comparatively more favourable results for certain software failure data structures where the frequency distribution of the cluster (clump) size of the software failures per week displays a negative exponential behaviour. Average relative error (ARE), mean squared error (MSE) and average Kolmogorov–Smirnov (K–S Av.D_n) statistics are used as measures of forecast quality for the proposed and competing parameter-estimation techniques in predicting the number of remaining future failures expected to occur until a target stopping time. Comparisons on five different simulated data sets that contain weekly recorded software failures are made to emphasize the advantages and disadvantages of the competing methods by means of the chronological prediction plots around the true target value and zero per cent relative error line. The proposed generalized compound Poisson (MLE and NLR) methods consistently produce more favourable predictions for those software failure data with negative exponential frequency distribution of the failure clump size versus number of weeks. Otherwise, the popularly used competing M–O log-Poisson model is a better fit for those data with a uniform clump size distribution to recognize the log-Poisson effect while the logarithm of the Poisson equation is a constant, hence uniform. The software analyst is urged to perform exploratory data analysis to recognize the nature of the software failure data before favouring a particular reliability estimation method. © 1997 by John Wiley & Sons, Ltd.     

二值量测误差FIR系统参数迭代辨识

本文考虑了量测数据为二值输出且含量测误差的一类有限脉冲响应(FIR)系统的参数辨识问题, 其中, 量测误差使得二值型量测值有一定概率得到相反的取值. 首先, 对所考虑的 FIR 系统, 给出了参数的极大似然估计(MLE), 证明了在噪声满足一定正则条件下MLE的强收敛性和渐近正态性. 此外, 通过分析似然函数的性质, 给出了一种基于期望最大化(EM)方法的MLE迭代求解算法. 为适应更一般的量测误差情形, 给出了带投影的迭代求解算法, 并从理论上证明了迭代估计序列的有界性. 进一步, 在给定数量的观测下, 得到了似然函数具有唯一最大值点的必要和充分条件, 并在持续激励输入条件下, 证明了迭代估计误差以指数速度收敛到零. 最后, 利用数值模拟结果验证了所提出算法的有效性.     

Comparison of variance-based and moment-independent global sensitivity analysis approaches by application to the SWAT model

Global Sensitivity Analysis (GSA) is an essential technique to support the calibration of environmental models by identifying the influential parameters (screening) and ranking them.In this paper, the widely-used variance-based method (Sobol') and the recently proposed moment-independent PAWN method for GSA are applied to the Soil and Water Assessment Tool (SWAT), and compared in terms of ranking and screening results of 26 SWAT parameters. In order to set a threshold for parameter screening, we propose the use of a “dummy parameter”, which has no influence on the model output. The sensitivity index of the dummy parameter is calculated from sampled data, without changing the model equations. We find that Sobol' and PAWN identify the same 12 influential parameters but rank them differently, and discuss how this result may be related to the limitations of the Sobol' method when the output distribution is asymmetric.