Diameter distributions in Pinus sylvestris L.stands:evaluating modelling approaches including a machine learning technique

The diameter distribution of trees in a stand provides the basis for determining the stand’s ecological and economic value,its structure and stability and appropriate management practices.Scots pine(Pinus sylvestris L.)is one of the most common and important conifers in Turkey,so a well-planned management schedule is critical.Diameter distribution models to accurately describe the stand structure help improve management strategies,but developing reliable models requires a deep understanding of the growth,output and constraints of the forests.The most important information derived by diameter distribution models is primary data on horizontal stand structure for each diameter class of trees:basal area and volume per unit area.These predictions are required to estimate the range of products and predicted volume and yield from a forest stand.Here,to construct an accurate,reliable diameter distribution model for natural Scots pine stands in the Türkmen Mountain region,we used Johnson’s SBdistribution to represent the empirical diameter distributions of the stands using ground-based measurements from 55 sample plots that included1219 trees in natural distribution zones of the forests.As an alternative,nonparametric approach,which does not require any predefined function,an artificial intelligence model was constructed based on support vector machine methodology.An error index was calculated to evaluate the results.Overall,both Johnson’s SB probability density function with a three-parameter recovery approach and the support vector regression methodology provided reliable estimates of the diameter distribution of these stands.

Modeling and forecasting exchange rate volatility in Bangladesh using GARCH models:a comparison based on normal and Student's t-error distribution

Background:Modeling exchange rate volatility has remained crucially important because of its diverse implications.This study aimed to address the issue of error distribution assumption in modeling and forecasting exchange rate volatility between the Bangladeshi taka(BDT)and the US dollar($).Methods:Using daily exchange rates for 7 years(January 1,2008,to April 30,2015),this study attempted to model dynamics following generalized autoregressive conditional heteroscedastic(GARCH),asymmetric power ARCH(APARCH),exponential generalized autoregressive conditional heteroscedstic(EGARCH),threshold generalized autoregressive conditional heteroscedstic(TGARCH),and integrated generalized autoregressive conditional heteroscedstic(IGARCH)processes under both normal and Student’s t-distribution assumptions for errors.Results and Conclusions:It was found that,in contrast with the normal distribution,the application of Student’s t-distribution for errors helped the models satisfy the diagnostic tests and show improved forecasting accuracy.With such error distribution for out-of-sample volatility forecasting,AR(2)–GARCH(1,1)is considered the best.

Gaussian-Student's t mixture distribution PHD robust filtering algorithm based on variational Bayesian inference

Aiming at the problem of filtering precision degradation caused by the random outliers of process noise and measurement noise in multi-target tracking(MTT) system,a new Gaussian-Student’s t mixture distribution probability hypothesis density(PHD) robust filtering algorithm based on variational Bayesian inference(GST-vbPHD) is proposed.Firstly,since it can accurately describe the heavy-tailed characteristics of noise with outliers,Gaussian-Student’s t mixture distribution is employed to model process noise and measurement noise respectively.Then Bernoulli random variable is introduced to correct the likelihood distribution of the mixture probability,leading hierarchical Gaussian distribution constructed by the Gaussian-Student’s t mixture distribution suitable to model non-stationary noise.Finally,the approximate solutions including target weights,measurement noise covariance and state estimation error covariance are obtained according to variational Bayesian inference approach.The simulation results show that,in the heavy-tailed noise environment,the proposed algorithm leads to strong improvements over the traditional PHD filter and the Student’s t distribution PHD filter.

基于T-S模糊逻辑的混合储能孤岛直流微电网功率分配控制

在含混合储能的直流微电网中,传统阻容下垂控制无法解决由线路电阻和负荷功率波动导致的系统功率分配失衡问题。为此,提出一种基于Takagi-Sugeno(T-S)模糊逻辑的自适应阻容下垂控制方法以实现混合储能的分频分配。根据蓄电池和超级电容的物理特性,建立单个蓄电池支路输出电压、蓄电池组间输出功率差额和阻性下垂系数之间的T-S模糊逻辑关系,以及单个超级电容支路输出功率及其变化率、超级电容组间功率差额和容性下垂系数之间的T-S模糊逻辑关系,并由此构建基于T-S模糊逻辑的阻容下垂控制器。推导含混合储能的直流微电网中各部分的平均阻抗模型,并采用阻抗比分析法对微电网的小信号稳定性进行研究。MATLAB/Simulink仿真结果表明,基于T-S模糊逻辑的阻容下垂控制可保证在线路电阻和负荷功率波动情况下系统功率的合理分配。

A Multivariate Student’s t-Distribution

A multivariate Student’s t-distribution is derived by analogy to the derivation of a multivariate normal (Gaussian) probability density function. This multivariate Student’s t-distribution can have different shape parameters for the marginal probability density functions of the multivariate distribution. Expressions for the probability density function, for the variances, and for the covariances of the multivariate t-distribution with arbitrary shape parameters for the marginals are given.

Effective Truncation of a Student’s <i>t</i>-Distribution by Truncation of the Chi Distribution in a Chi-Normal Mixture

A Student’s t-distribution is obtained from a weighted average over the standard deviation of a normal distribution, σ, when 1/σ is distributed as chi. Left truncation at q of the chi distribution in the mixing integral leads to an effectively truncated Student’s t-distribution with tails that decay as exp (-q2t2). The effect of truncation of the chi distribution in a chi-normal mixture is investigated and expressions for the pdf, the variance, and the kurtosis of the t-like distribution that arises from the mixture of a left-truncated chi and a normal distribution are given for selected degrees of freedom 5. This work has value in pricing financial assets, in understanding the Student’s t--distribution, in statistical inference, and in analysis of data.

基于t-SNE的多参数岩体结构面分步聚类方法

结构面聚类是进行岩体稳定性评价的重要步骤。常用聚类方法多以产状作为分组依据,忽略了结构面物理特性指标对岩体稳定性的影响。针对分组依据单一化的不足,综合考虑结构面倾向、倾角、迹长、张开度、填充状态和粗糙度的影响,提出一种基于学生分布随机邻近嵌入(student-distributed stochastic neighbor embedding,简称t-SNE)的多参数岩体结构面分步聚类方法。首先,利用t-SNE算法对除产状外的结构面特征进行数据降维;进而利用模拟退火算法搜索K-means算法的全局最优初始值,并采用分步聚类思想完成聚类。研究表明:所提方法有效地解决了高维空间样本稀疏的问题,同时保留了数据的局部结构与全局结构。新方法相比于传统方法能对空间分布相似区内结构面的物理特性进行精确划分,分组精度更高,且在避免复杂权重值计算的条件下,能有效区分产状与物理特性参数对岩体稳定性的影响差异。最后,将所提方法应用于中国新疆某露天矿坡结构面实测数据分析中,所得分组结果合理可靠,进一步证明该方法在实际工程中的有效性。研究方法可为多参数岩体结构面的分步聚类提供参考。

厚尾噪声条件下星凸形扩展目标student’s t滤波器

针对非线性非高斯厚尾噪声条件下的不规则形状的扩展目标跟踪问题,提出了基于随机超曲面模型(RHM)的星凸形扩展目标student’s t滤波算法.首先,在带有非高斯厚尾过程噪声和厚尾量测噪声的系统中,基于student’s t分布给出鲁棒student’s t滤波器.其次,利用随机超曲面模型描述任意星凸形扩展目标的量测源分布,提出带厚尾噪声的星凸形扩展目标student’s t滤波器.最后通过仿真验证了所提方法的正确性和有效性.

基于Student′s t分布的不依赖子波最小二乘逆时偏移

最小二乘逆时偏移(Least-Squares Reverse Time Migration,LSRTM)与常规偏移相比具有更高的成像分辨率、振幅保真性及均衡性等优势,是当前研究的热点之一.震源子波的估计直接影响LSRTM结果的好坏,在实际情况下考虑到震源子波的空变特性,其估计十分困难.为了消除子波对LSRTM结果的影响,本文发展了基于卷积目标泛函的不依赖子波LSRTM算法.目标泛函由观测记录卷积模拟记录的参考道以及模拟记录卷积观测记录的参考道组成,由于观测子波和模拟子波在目标泛函的两项中同时存在,从而消除了子波的影响.此外,常用的基于L2范数拟合的LSRTM算法对噪声非常敏感,尤其是当地震数据中含有异常值时,常规LSRTM无法得到满意的结果.Student′s t分布相比L2范数具有更好的稳健性,本文将其推广到不依赖子波LSRTM中,提升了算法的稳健性,最后通过理论模型及实际资料试算验证了算法的有效性和对复杂模型的适应性.

Student’s t滤波框架下的信息融合算法

针对多传感器系统的观测噪声为非高斯噪声的问题,通过Student’s t滤波框架和四元数特性相结合,以无迹变换计算Student’s t加权积分函数,设计基于Student’s t分布的无迹四元数滤波算法,作为局部滤波算法.利用拉格朗日乘子法计算最优融合权重系数,通过线性加权融合的方式,对各局部滤波结果进行融合.采用基于四元数的目标姿态运动模型进行仿真,利用3个星敏感器同时对同一目标进行观测,通过与已有的鲁棒无迹Student’s t滤波(RSTUF)算法对比,验证所提算法的有效性.仿真结果表明:所提算法在对目标姿态的估计精度、滤波收敛速度及收敛后的数值稳定性方面均高于RSTUF算法;通过多个观测信息互补,提高了估计精度及容错性.

量测随机延迟下带厚尾噪声的鲁棒Student’s t随机容积卡尔曼滤波器

针对量测随机延迟下带厚尾过程噪声和量测噪声的非线性状态估计问题,本文通过充分考虑量测一步随机延迟特性及过程噪声和量测噪声的“厚尾”特性,推导了一种新的鲁棒Student’s t滤波器框架,并采用随机Student’s t-球面相径容积规则近似计算Student’s t权值积分,从而设计了一种新的鲁棒Student’s t随机容积滤波器.首先,采用一组服从伯努利分布的随机序列来描述系统中可能存在的量测一步随机延迟现象,并采用Student’s t分布刻画过程噪声和量测噪声中存在的“厚尾”特性;其次,从理论上证明了当自由度参数趋于无穷以及随机延迟概率为零时,该鲁棒Student’s t滤波器就自动地降为标准的非线性高斯近似滤波器;最后,采用随机Student’s t-球面相径容积规则给出了一种新的鲁棒Student’s t随机容积滤波器,并通过协同转弯模型验证了该滤波器的有效性和优越性.

非对称三参数Student-t分布的参数估计及应用

文章基于t分布构造了一个新的非对称三参数Student-t分布。推导了新分布的累计分布函数、分位数函数、随机变量表达式和原点矩估计等基础性质,使用了矩方法、极大似然估计法和贝叶斯估计法等进行了参数估计,并通过生成模拟数据的方法比较验证了三种方法的合理性。最后,将新分布代入实例中拟合,结果表明新分布相比其他的分布,在非对称和厚尾方面具有更好的拟合能力。

基于Student-t分布的混合模型图像分割方法

传统图像分割方法在分割被重尾噪声污染的图像时的分割效果不理想。针对该问题,提出一种基于Student-t分布的图像分割方法。该方法根据像素间的空间关系,计算出其先验概率,使用梯度下降法优化参数,从而最小化误差函数,在参数优化后得到像素点的后验概率值,对像素进行标记以实现图像分割。实验结果表明,在处理被重尾噪声腐蚀的图像时,与传统的K-均值、模糊C-均值等图像分割方法相比,该方法的误分率较低,分割效果较好。

带厚尾噪声的鲁棒Student’s t容积滤波器

为了解决带厚尾过程和量测噪声的非线性状态估计问题,本文提出了一种新的鲁棒非线性滤波器.首先,对带厚尾过程和量测噪声的非线性系统进行了数学建模,并推导了基于Student’s t近似的鲁棒非线性滤波器(RSTNF)的一般结构.其次,针对RSTNF中涉及到的含有关于Student’s t分布的多维非线性函数积分的求解问题,提出了基于Student’s t分布的球径容积准则(STSRCR),并在此基础上设计了一种新的鲁棒Student’s t容积滤波器(RSTCF).最后,利用目标跟踪仿真验证了本文提出的带厚尾噪声的RSTCF的有效性以及与现有方法相比的优越性.

Student’s t Increments

Some moments and limiting properties of independent Student’s t increments are studied. Inde-pendent Student’s t increments are independent draws from not-truncated, truncated, and effectively truncated Student’s t-distributions with shape parameters and can be used to create random walks. It is found that sample paths created from truncated and effectively truncated Student’s t-distributions are continuous. Sample paths for Student’s t-distributions are also continuous. Student’s t increments should thus be useful in construction of stochastic processes and as noise driving terms in Langevin equations.

应用T-S模糊方法对铁磁谐振过电压的混沌抑制

抑制和控制铁磁谐振过电压对实现智能电网中重要的"自愈"功能具有重要的意义。为此,运用非线性动力学理论于抑制中性点接地系统所发生的具有混沌效应的铁磁谐振。通过分析铁磁谐振电路所表现出的混沌特性,并针对电力系统中参数无法完全已知的限制,首次提出建立谐振系统的T-S模糊模型,制定合适的模糊规则,并应用平行分布补偿法设计模糊控制器来抑制铁磁谐振过电压,以达到迅速控制的良好效果。另外,通过Lya-punov理论验证了该控制器符合系统稳定性要求。仿真结果也验证了该方法的有效性,同时克服了传统方法对参数完全精确已知的限制。

T-S模糊广义系统研究综述

对目前T-S模糊广义系统的研究成果加以总结.主要讨论了T-S模糊广义系统的分析、综合与应用的问题,并对这一研究领域仍需解决的问题和未来的发展方向作了进一步的展望.

航空发动机T-S分布式系统自适应鲁棒滑模控制

为提高航空发动机非线性不确定分布式控制系统的鲁棒性,考虑参数摄动,外部干扰,随机时延的影响,采用一种基于飞行包线划分的航空发动机T-S模糊模型,进行了鲁棒自适应滑模控制方法的研究。基于鲁棒H∞理论,针对模糊规则的状态空间模型,推导了滑模运动渐进稳定的充分条件,设计具有扰动抑制性能的鲁棒滑模面;基于并行分布补偿技术,采用与T-S模型相同的模糊规则,确定全局模糊滑模控制器设计策略,在此基础上,采用自适应技术估计未知干扰上界,设计了自适应滑模控制器,并证明了系统在控制器作用下的到达性。仿真结果表明该方法能够保证系统渐进稳定,对所考虑的不确定性因素鲁棒性较好,有效削弱了抖振,对不同工作点和干扰条件具有良好的适应性。

混沌系统基于T-S模糊模型的控制方法

将模糊控制技术应用于混沌控制中,可以克服反馈线性化等传统方法对参数完全精确已知的限制;用T-S模糊系统来逼近非线性系统,它的IF-THEN规则后件由线性状态空间子系统构成,进而可以应用模糊系统的控制理论求得模糊控制器,用此非线性控制器来控制非线性系统,以求良好的控制效果;模糊规则后件部分以局部线性方程形式给出的T-S模糊模型可以通过调整相关参数很好地逼近混沌系统,基于该模型采用平行分散补偿技术设计出具有相同规则数目的模糊控制器,控制器所有参数可以通过求解一组线性矩阵不等式一次性得到。仿真结果验证了该方法的有效性。