A laboratory study of directional spectra with maximum likelihood method─I Developing wind wave

From measurements by a circular array consisting of 18 wave gauges in a large wave tank, directional spectra of wind-generated waves in deep water are systematically determined by using maximum likehood method.The investigations reveal that the angular spreading of the wave energy is consistent with cos2s(θ/2) proposed by Longuet-Higgins et al. (1963, Ocean Wad Spectra,11~136), if the bimodal distributions of wave energy are not taken into account. Bimodality occurring on higher frequency than peak frequency is too rare to affect our whole results. Surprisingly, a much broader directional spreading than that of the field, which is interpreted by the strongly nonlinear energy transfer because of the very young waves in laboratory, is found. The parameter s depends on frequency in the same way as observed by Mitsuyasu et al. (1975, Journal of Physical Oceanography, 5, 750~760)and Hasselmann et al. (1980, Journal of physical Oceanography, 10, 1264~1280) in the field, and the relationship between the four nondimensional parameters sm, fo, b1 and b2, determining the directional width, and (corresponding to the inverse of wave age) are given respectively. The observed distributions are found to agree well with the suggestion of Donelan et al. (1985, Philosophical Transaction of Royal Society of London, A315, 509~562) when applied to field waves.

A Maximum Likelihood Method for Estimating Probabilistic Strain Amplitude-Fatigue Life Curves

The fatigue lives of materials and structures at different strain levels show het- eroscedasticity. In addition when the number of test specimens is insufficient, the fatigue strength coefficient and fatigue ductility coefficient of the fitting parameters in the total strain life equa- tion may not have definite physical significance. In this work, a maximum likelihood method for estimating probabilistic strain amplitude fatigue life curves is presented based on the fatigue lives at different strain levels. The proposed method is based on the general basic assumption that the logarithm of fatigue life at an arbitrary strain level is normally distributed. The rela- tionship among the parameters of total strain life equation, monotonic ultimate tensile stress and percentage reduction of area is adopted. The presented approach is finally illustrated by two applications. It is shown that probabilistic strain amplitude-fatigue life curves can be eas- ily estimated based on the maximum likelihood method. The results show that fatigue lives at different strain levels have heteroscedasticity and the values of fatigue strength coefficient and fatigue ductility coefficient obtained by the proposed method are close to those of the true tensile fracture stress and true tensile fracture strain.

Maximum likelihood spectrum estimation method and its application in seismo－magnet－icrelation

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CONVERGENCE OF ITERATION METHODS OF MAXIMUM LIKELIHOOD ESTIMATOR AND ITS APPLICATIONS

Iteration methods and their convergences of the maximum likelihoodestimator are discussed in this paper.We study Gauss-Newton method and give a set ofsufficient conditions for the convergence of asymptotic numerical stability.The modifiedGauss-Newton method is also studied and the sufficient conditions of the convergence arepresented.Two numerical examples are given to illustrate our results.

A Study of EM Algorithm as an Imputation Method: A Model-Based Simulation Study with Application to a Synthetic Compositional Data

Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.

A laboratory study of directional spectrawith maximum likelihood mehod─ⅡDecaying swell

From measurements by a circular array consisting of 18 wave gauges in a large wave tank, directional spectra of swell in deep water are systematically investigated with maximum likelihood method. It is shown that the directional spreading of swell, qualitatively similar to that of developing wind wave which is narrowest in the region of Peak frequency and bxoadens with increasing or decreasing frequency, can be effectively described by cos2s(θ/2) introduced by Longuet-Higgins et al. (1963,Ocean Wave Spectra, 111~136). It is intriguing that bimodal distribution found in our experiments appers at the forward face instead of the rear face of a frequency spectrum in the cases of nonlinearity being very weak. Parameterized by nonlinearity, formulations which can be applied to swell as well as wind wave are proposed. It is concluded that nonlinear interaction plays a central role in controlling the development of directional angular spreading even for the swell.

Maximum Likelihood Estimation of the Identification Parameters and Its Correction

By taking the subsequence out of the input-output sequence of a system polluted by white noise, an independent observation sequence and its probability density are obtained and then a maximum likelihood estimation of the identification parameters is given. In order to decrease the asymptotic error, a corrector of maximum likelihood (CML) estimation with its recursive algorithm is given. It has been proved that the corrector has smaller asymptotic error than the least square methods. A simulation example shows that the corrector of maximum likelihood estimation is of higher approximating precision to the true parameters than the least square methods.

On the Maximum Likelihood and Least Squares Estimation for the Inverse Weibull Parameters with Progressively First-Failure Censoring

In this article, we consider a new life test scheme called a progressively first-failure censoring scheme introduced by Wu and Kus [1]. Based on this type of censoring, the maximum likelihood, approximate maximum likelihood and the least squares method estimators for the unknown parameters of the inverse Weibull distribution are derived. A comparison between these estimators is provided by using extensive simulation and two criteria, namely, absolute bias and mean squared error. It is concluded that the estimators based on the least squares method are superior compared to the maximum likelihood and the approximate maximum likelihood estimators. Real life data example is provided to illustrate our proposed estimators.

利用微卫星标记鉴定核桃杂交子代的亲本

杂交育种是目前核桃育种的主要方法,为了快速有效地鉴别杂交子代的真实性,加速杂交育种进程,利用微卫星标记方法辅助进行核桃亲子鉴定。研究从已发表的60对核桃属植物微卫星标记中筛选出12个多态性相对较高且稳定扩增的微卫星位点,对5个杂交组合子代159个个体通过基因型排除法和最大似然法进行亲子关系鉴定。基因型排除法鉴定出121个子代的正确亲本,鉴定率较高,总鉴定率76.10%;最大似然法亲权分析显示,双亲未知情形达到置信区间预测出正确亲本的子代有12个,总鉴定率7.55%。父本未知情形达到置信区间推算出正确亲本的子代有19个,总体鉴定率11.95%。整体鉴定率较低。

基于波束空间交替投影极大似然的拖曳式诱饵分辨判别方法

机载平台在遭遇威胁时,通过释放拖曳式诱饵假目标干扰进行自卫.载机和拖曳式诱饵在雷达波束宽度内,且径向距离小于距离分辨率时,雷达无法通过常规方法对载机目标和拖曳式诱饵进行分辨测量.针对数字相控阵雷达同拖曳式诱饵对抗的问题,提出一种基于波束空间交替投影极大似然(BSAP-ML)方法.首先通过阵元空间到波束空间处理,减少数字相控阵维度;然后通过交替投影方法对目标和拖曳式诱饵的角度进行迭代测量;最后通过基于角度向量的判别方法对载机目标和诱饵进行判断识别.仿真结果表明,该方法可用于数字相控阵雷达,对载机和拖曳式诱饵进行有效的超分辨角度测量和判别.

一种动态不确定海洋环境下的USV态势自主感知及避障算法

针对无人艇在动态不确定海洋环境下的态势自主感知和实时避障问题,提出了一种遵守COLREGs海事规则,且考虑传感器测量误差和障碍物随机运动不确定信息的无人艇航行态势自主感知及避障算法。阐述了无人艇在海上航行时须遵守的3类海事规则,追越、交叉相遇和正面相遇;考虑到传感器存在的测量误差、观测漂移以及障碍物运动的随机不确定性,对相关误差进行建模,并基于融合COLREGs规则的速度障碍法,设计提出了一种融合COLREGs海事规则的USV态势自主感知及避障算法;通过正面相遇、追越、左右交叉相遇4种典型场景下的仿真实验,验证了所提出算法的有效性。

基于改进权函数距离的机器人运动偏差补偿算法设计

针对机器人在组装和生产过程中,由于几何参数存在一定误差,使连杆以及关节处等不可避免地出现细微差别,对机器人运动精度产生一定影响问题,提出了基于改进权函数距离的机器人运动偏差补偿算法设计方案。在定位机器人位置前添加扭角,获取机器人两坐标系间转换矩阵,根据线性标定计算机器人运动定位的绝对误差,利用改进权函数建立机器人距离误差数学模型,初步补偿运动误差。计算机器人末端执行器中心点位置和姿态的偏差,将补偿问题转化成机器人运动优化问题,得出运动偏差优化问题目标函数,经多次迭代得出最终补偿结果。实验结果表明,所提方法的误差补偿效果佳,重心补偿后的机器人运行稳定性好。

基于多应用场景的改进DV-Hop定位模型

针对距离矢量跳(DV-Hop)定位模型定位精度低、优化策略场景依赖性强的问题,提出一种基于函数分析和模拟定参的改进DV-Hop模型——函数修正距离矢量跳(FuncDV-Hop)定位模型。首先,分析DV-Hop模型的平均跳距、距离估计和最小二乘法中的误差原因,引入待定系数优化、阶跃函数分段实验、带等效点的权重函数策略和极大似然估计修正;其次,考虑多应用场景,用控制变量法,分别将总节点数、信标节点比例、通信半径、信标节点数和待测节点数作为变量,设计对照实验;最后,进行仿真定参和整合优化测试两阶段实验,最终的改进策略较原DV-Hop模型的定位精度提高了23.70%~75.76%,平均优化率57.23%。实验结果表明,FuncDV-Hop模型的优化率最高达到了50.73%,与基于遗传算法和神经动力学改进的DV-Hop模型相比,FuncDV-Hop模型的优化率提升了0.55%~18.77%。所提模型不引入其他参量,不增加无线传感器网络(WSN)的协议开销,且有效提高定位精度。

基于威布尔分布的风功率密度计算方法比较

[目的]风功率密度是风资源评估重要参数之一,准确地计算风功率密度有赖于风频威布尔分布拟合的准确性,对它进行正确地分析和评估有助于降低投资风险和提高投资决策的可靠性。针对目前风资源评估缺少威布尔分布拟合准确性方面的研究,文章旨通过研究比较那种威布尔分布拟合具有较高的精度,从而提高风资源评估的准确性。[方法]对目前国内外采用的5种威布尔模拟风频分布的方法进行研究,引入决定系数来确定威布尔模拟的准确度,比较威布尔函数计算风功率密度与实测数据计算风功率密度绝对误差和相对误差大小。[结果]结果表明:能量因子法EPF和最大似然法MLE模拟出来的威布尔拟合决定系数高于其他方法,包括经验法(EPJ和EPL)和最小二乘法(LLSA)。用这两种方法所得的参数计算风功率密度,与实测数据计算所得的风功率密度相比较,其绝对误差和相对误差也小于其他3种方法。[结论]研究结果可为风资源评估时选择何种威布尔方法计算风功率密度提供参考依据,客观地反应风电场风资源情况,提高风资源评估的准确性。

长记忆时间序列的均值单变点估计

文章采用拟极大似然法估计了一类长记忆时间序列模型的单均值变点,在变点大小固定和变点收缩两种情形下分析了估计量的渐近性质。研究发现,变点大小与长记忆性之间存在一种权衡关系。具体而言,当变点大小固定时,变点估计量是不相合的,而变分点估计量是T-相合的;当变点收缩时,变点估计量的收敛速度依赖于记忆参数d,估计量的极限分布得以推导。最后,蒙特卡洛实验和实证分析验证了所提理论结果的有限样本表现。

Importance Sampling Method in V-Space

Based on the observation of importance sampling and second order information about the failure surface of a structure, an importance sampling region is defined in V-space which is obtained by rotating a U-space at the point of maximum likelihood. The sampling region is a hyper-ellipsoid that consists of the sampling ellipse on each plane of main curvature in V-space. Thus, the sampling probability density function can be constructed by the sampling region center and ellipsoid axes. Several examples have shown the efficiency and generality of this method.

Singularity of Some Software Reliability Models and Parameter Estimation Method

According to the principle, “The failure data is the basis of software reliability analysis”, we built a software reliability expert system (SRES) by adopting the artificial intelligence technology. By reasoning out the conclusion from the fitting results of failure data of a software project, the SRES can recommend users “the most suitable model” as a software reliability measurement model. We believe that the SRES can overcome the inconsistency in applications of software reliability models well. We report investigation results of singularity and parameter estimation methods of experimental models in SRES.

Simulation Methods of Stochastic Volatility Interest Rate Term Structure

A term structure model bearing features of stochastic volatility and stochastic mean drift with jump （SVJ-SD model for short） is built in the paper to describe the stochastic behavior of interest rates.Based on sample data of an interest rate of national bond repurchase,maximum likelihood （ML）,linear Kalman filter and efficient method of moments （EMM） are used to estimate the model.While ML works well for simple models,it may lead to considerable deviation in parameter estimation when dynamic risks of interest rates are considered in them.Linear Kalman filter is a tractable and reasonably accurate technique for estimation cases where ML was not feasible.Moreover,when compared with the first two approaches,using EMM can obtain better parameter estimates for complex models with non-affine structures.

定时截尾样本下广义逆指数分布参数的Bayes估计

文章在定时截尾样本下,讨论了广义逆指数分布形状参数、可靠度和危险率的极大似然估计。基于指数先验分布,在熵损失、平方损失和Linex损失函数下分别得到形状参数、可靠度和危险率的Bayes估计,并给出了确定超参数的方法。利用数值模拟计算了估计量的各种估计均值和均方误差,研究结果表明,形状参数在熵损失和Linex损失函数下的估计精度较高;可靠度的Bayes估计整体优于极大似然估计;危险率的Bayes估计在Linex损失函数下的效果较好。

基于数据量化分析的动态视觉景观规划仿真

为提升景观规划效用,提出基于数据量化分析的动态视觉景观规划。以数据量化分析作为动态视觉景观规划计算手段,通过人均绿地的面积、绿地率、多样性的指数、优势度指数、均匀度指数、破碎度的指数、分离度指数、分维度指数、连通性指数得到景观空间格局指标,再利用城市景观可达性、景观服务效率、人口密度、城市路网、景观绿地形状实现数据量化分析。同时以角二阶矩、相关系数、信息熵以及对比度四种纹理特征描述景观系统图像纹理,采用最大似然法分类完成动态景观整体布局规划。仿真结果证明:所提方法系统性研究相关数据,可精准表达规划设计细节,有效改善地区生态环境,降低空气污染,可作为现实景观规划理论基础。