Predicting carbon storage of mixed broadleaf forests based on the finite mixture model incorporating stand factors,site quality,and aridity index

The diameter distribution function(DDF)is a crucial tool for accurately predicting stand carbon storage(CS).The current key issue,however,is how to construct a high-precision DDF based on stand factors,site quality,and aridity index to predict stand CS in multi-species mixed forests with complex structures.This study used data from70 survey plots for mixed broadleaf Populus davidiana and Betula platyphylla forests in the Mulan Rangeland State Forest,Hebei Province,China,to construct the DDF based on maximum likelihood estimation and finite mixture model(FMM).Ordinary least squares(OLS),linear seemingly unrelated regression(LSUR),and back propagation neural network(BPNN)were used to investigate the influences of stand factors,site quality,and aridity index on the shape and scale parameters of DDF and predicted stand CS of mixed broadleaf forests.The results showed that FMM accurately described the stand-level diameter distribution of the mixed P.davidiana and B.platyphylla forests;whereas the Weibull function constructed by MLE was more accurate in describing species-level diameter distribution.The combined variable of quadratic mean diameter(Dq),stand basal area(BA),and site quality improved the accuracy of the shape parameter models of FMM;the combined variable of Dq,BA,and De Martonne aridity index improved the accuracy of the scale parameter models.Compared to OLS and LSUR,the BPNN had higher accuracy in the re-parameterization process of FMM.OLS,LSUR,and BPNN overestimated the CS of P.davidiana but underestimated the CS of B.platyphylla in the large diameter classes(DBH≥18 cm).BPNN accurately estimated stand-and species-level CS,but it was more suitable for estimating stand-level CS compared to species-level CS,thereby providing a scientific basis for the optimization of stand structure and assessment of carbon sequestration capacity in mixed broadleaf forests.

Finite Mixture of Heteroscedastic Single-Index Models

In many applications a heterogeneous population consists of several subpopulations. When each subpopulation can be adequately modeled by a heteroscedastic single-index model, the whole population is characterized by a finite mixture of heteroscedastic single-index models. In this article, we propose an estimation algorithm for fitting this model, and discuss the implementation in detail. Simulation studies are used to demonstrate the performance of the algorithm, and a real example is used to illustrate the application of the model.

A Weighted Spatially Constrained Finite Mixture Model for Image Segmentation

Spatially Constrained Mixture Model(SCMM)is an image segmentation model that works over the framework of maximum a-posteriori and Markov Random Field(MAP-MRF).It developed its own maximization step to be used within this framework.This research has proposed an improvement in the SCMM’s maximization step for segmenting simulated brain Magnetic Resonance Images(MRIs).The improved model is named as the Weighted Spatially Constrained Finite Mixture Model(WSCFMM).To compare the performance of SCMM and WSCFMM,simulated T1-Weighted normal MRIs were segmented.A region of interest(ROI)was extracted from segmented images.The similarity level between the extracted ROI and the ground truth(GT)was found by using the Jaccard and Dice similarity measuring method.According to the Jaccard similarity measuring method,WSCFMM showed an overall improvement of 4.72%,whereas the Dice similarity measuring method provided an overall improvement of 2.65%against the SCMM.Besides,WSCFMM signicantly stabilized and reduced the execution time by showing an improvement of 83.71%.The study concludes that WSCFMM is a stable model and performs better as compared to the SCMM in noisy and noise-free environments.

A Finite Mixture of Generalised Inverse Gaussian with Indexes -1/2 and -3/2 as Mixing Distribution for Normal Variance Mean Mixture with Application

Mixture models have become more popular in modelling compared to standard distributions. The mixing distributions play a role in capturing the variability of the random variable in the conditional distribution. Studies have lately focused on finite mixture models as mixing distributions in the mixing mechanism. In the present work, we consider a Normal Variance Mean mixture model. The mixing distribution is a finite mixture of two special cases of Generalised Inverse Gaussian distribution with indexes -1/2 and -3/2. The parameters of the mixed model are obtained via the Expectation-Maximization (EM) algorithm. The iterative scheme is based on a presentation of the normal equations. An application to some financial data has been done.

Modeling Cyber Loss Severity Using a Spliced Regression Distribution with Mixture Components

Cyber losses in terms of number of records breached under cyber incidents commonly feature a significant portion of zeros, specific characteristics of mid-range losses and large losses, which make it hard to model the whole range of the losses using a standard loss distribution. We tackle this modeling problem by proposing a three-component spliced regression model that can simultaneously model zeros, moderate and large losses and consider heterogeneous effects in mixture components. To apply our proposed model to Privacy Right Clearinghouse (PRC) data breach chronology, we segment geographical groups using unsupervised cluster analysis, and utilize a covariate-dependent probability to model zero losses, finite mixture distributions for moderate body and an extreme value distribution for large losses capturing the heavy-tailed nature of the loss data. Parameters and coefficients are estimated using the Expectation-Maximization (EM) algorithm. Combining with our frequency model (generalized linear mixed model) for data breaches, aggregate loss distributions are investigated and applications on cyber insurance pricing and risk management are discussed.

Mechanical Properties of Soil-Rock Mixture Filling in Fault Zone Based on Mesostructure

Soil-rock mixture(SRM)filling in fault zone is an inhomogeneous geomaterial,which is composed of soil and rock block.It controls the deformation and stability of the abutment and dam foundation,and threatens the long-term safety of high arch dams.To study the macroscopic and mesoscopic mechanical properties of SRM,the development of a viable mesoscopic numerical simulation method with a mesoscopic model generation technology,and a reasonable parametric model is crucially desired to overcome the limitations of experimental conditions,specimen dimensions,and experiment fund.To this end,this study presents a mesoscopic numerical method for simulating the mechanical behavior of SRM by proposing mesoscopic model generation technology based on its mesostructure features,and a rock parameter model considering size effect.The validity and rationality of the presented mesoscopic numerical method is experimentally verified by the triaxial compression tests with different rock block contents(RBC).The results indicate that the rock block can increase the strength of SRM,and it is proved that the random generation technique and the rock parameter model considering size effect are validated.Furthermore,there are multiple failure surfaces for inhomogeneous geomaterial of SRM,and the angle of the failure zone is no longer 45◦.The yielding zones of the specimen are more likely to occur in thin sections of soil matrix isolated by blocks with the failure path avoiding the rock block.The proposed numerical method is effective to investigate the meso-damage mechanism of SRM.

A Special Weight for Inverse Gaussian Mixing Distribution in Normal Variance Mean Mixture with Application

Normal Variance-Mean Mixture (NVMM) provides a general framework for deriving models with desirable properties for modelling financial market variables such as exchange rates, equity prices, and interest rates measured over short time intervals, i.e. daily or weekly. Such data sets are characterized by non-normality and are usually skewed, fat-tailed and exhibit excess kurtosis. The Generalised Hyperbolic distribution (GHD) introduced by Barndorff-Nielsen (1977) which act as Normal variance-mean mixtures with Generalised Inverse Gaussian (GIG) mixing distribution nest a number of special and limiting case distributions. The Normal Inverse Gaussian (NIG) distribution is obtained when the Inverse Gaussian is the mixing distribution, i.e., the index parameter of the GIG is . The NIG is very popular because of its analytical tractability. In the mixing mechanism, the mixing distribution characterizes the prior information of the random variable of the conditional distribution. Therefore, considering finite mixture models is one way of extending the work. The GIG is a three parameter distribution denoted by and nest several special and limiting cases. When , we have which is called an Inverse Gaussian (IG) distribution. When , , , we have , and distributions respectively. These distributions are related to and are called weighted inverse Gaussian distributions. In this work, we consider a finite mixture of and and show that the mixture is also a weighted Inverse Gaussian distribution and use it to construct a NVMM. Due to the complexity of the likelihood, direct maximization is difficult. An EM type algorithm is provided for the Maximum Likelihood estimation of the parameters of the proposed model. We adopt an iterative scheme which is not based on explicit solution to the normal equations. This subtle approach reduces the computational difficulty of solving the complicated quantities involved directly to designing an iterative scheme based on a representation of the normal equation. The algorithm is easily programmable and we obtained a monotonic convergence for the data sets used.

Log-cumulants of the finite mixture model and their application to statistical analysis of fully polarimetric UAVSAR data

Since its first flight in 2007,the UAVSAR instrument of NASA has acquired a large number of fully Polarimetric SAR(PolSAR)data in very high spatial resolution.It is possible to observe small spatial features in this type of data,offering the opportunity to explore structures in the images.In general,the structured scenes would present multimodal or spiky histograms.The finite mixture model has great advantages in modeling data with irregular histograms.In this paper,a type of important statistics called log-cumulants,which could be used to design parameter estimator or goodness-of-fit tests,are derived for the finite mixture model.They are compared with logcumulants of the texture models.The results are adopted to UAVSAR data analysis to determine which model is better for different land types.

Local component based principal component analysis model for multimode process monitoring

For plant-wide processes with multiple operating conditions,the multimode feature imposes some challenges to conventional monitoring techniques.Hence,to solve this problem,this paper provides a novel local component based principal component analysis(LCPCA)approach for monitoring the status of a multimode process.In LCPCA,the process prior knowledge of mode division is not required and it purely based on the process data.Firstly,LCPCA divides the processes data into multiple local components using finite Gaussian mixture model mixture(FGMM).Then,calculating the posterior probability is applied to determine each sample belonging to which local component.After that,the local component information(such as mean and standard deviation)is used to standardize each sample of local component.Finally,the standardized samples of each local component are combined to train PCA monitoring model.Based on the PCA monitoring model,two monitoring statistics T^(2) and SPE are used for monitoring multimode processes.Through a numerical example and the Tennessee Eastman(TE)process,the monitoring result demonstrates that LCPCA outperformed conventional PCA and LNS-PCA in the fault detection rate.

基于FMM算法的我国寒潮路径分类及气候特征分析

利用1965—2015年冬半年寒潮过程数据和NCEP/NCAR再分析资料,通过FMM算法聚类分析,将影响我国寒潮路径确定为4类,并统计分析了不同类型路径寒潮的活动变化趋势以及环流特征。研究结果表明:各类路径寒潮的频数、强度、季节分布和年际变化存在显著差异,第一类西路转向型寒潮频数最多且逐年减少趋势最大,第三类西北型寒潮强度最大,第四类西路型寒潮在春季频发且变化趋势平缓;在寒潮爆发时刻,500 h Pa温压场配置、风场转变、高层涡度平流和冷暖平流以及地面冷高压分布与寒潮路径的选择密切相关,其中第二类北路型寒潮的低槽、负涡度区和冷平流区偏东分布,第三类则相应偏西。

季冻区OGFC沥青混合料车辙预估模型研究

目的研究季冻区OGFC沥青混合料的高温抗车辙能力,建立车辙预估模型,推广OGFC沥青混合料在季冻区的应用。方法采用车辙试验系统进行车辙试验,分析轴载作用次数、试件高度、温度、抗剪强度、冻融循环次数对OGFC沥青混合料车辙深度的影响;基于经验法建立季冻区OGFC沥青混合料车辙预估模型,通过最小二乘法拟合模型参数,对建立的预估模型进行室内试验验证以及有限元对比分析。结果各影响因素与车辙深度呈现幂函数关系,冻融循环作用加速车辙形成,室内试验实测车辙深度与模型预估的车辙深度相对误差为0.11%~9.81%。结论经验法建立的季冻区OGFC沥青混合料车辙预估模型预估精度较高,预估模型误差受试验条件和材料参数影响,其中材料参数影响较明显。

我国省级经济周期波动的同步性研究

省级经济周期波动研究对促进区域协同发展、维持经济的可持续发展和助力经济高质量发展具有重要意义。将实际GDP增长率视为经济周期波动,基于时变相关系数测算我国2005—2023年31个省份的经济周期波动同步性,分析其时变特征,借助时变一致度指数和FMM聚类,从周期阶段视角深入探究周期波动同步性的变动原因,并分析不同宏观经济因素对经济周期波动同步性的影响。研究发现:第一,在样本期内,我国省级经济周期波动的同步性呈现出先上升,再下降,然后再上升,最后趋于稳定的趋势变化。其中,2011年2季度至2019年4季度的经济周期波动同步性经历了初期缓慢、中期加速、后期稳定的阶段性下滑;2020年后,经济周期波动同步性快速提升,并在较高水平上保持稳定。在多个时间段,存在与其他省份经济周期波动同步性有较大差异的关键省份。产业结构异质性可能是这些差异出现的主要原因。第二,在同步性下降阶段,各省份周期阶段的时间错位程度有所增加,但形态特征差异才是下滑的主要因素。以各省份平均周期阶段形态特征为依据,通过聚类分析,除湖北因新冠疫情影响被单独划分为一类外,其余省份被划分为短周期低波动和长周期高波动两类。前者所含省份普遍有相对更强的经济韧性或更多元的产业布局,后者所含省份通常受全球经济发展态势影响较大或产业结构布局相对单一。属于同一类别的省份并无显著的地域特征。第三,实证研究表明,地理距离的拉近并不能显著提升各省份的经济周期波动同步性。放松地域限制后,属于同一周期阶段形态特征类别的省份经济周期波动同步性更高。经济规模、收入差距、产业结构相似度、物价水平差异、财政政策差异和对外贸易差异均会对经济周期波动的同步性产生影响。但在同步性的上升、下降和稳定阶段,具有显著影响的宏观因素存在一定差别。经济规模以及产业结构相似度的提升在任何阶段均会显著提高经济周期波动同步性。基于此,应坚持推动各省产业多元化发展,加强区域内周期差异化省份的协调合作,助力经济高质量发展。

基于CMOD法的沥青混合料抗裂性能评价方法仿真

为了降低评价结果与实测结果之间的误差,提出基于CMOD法的沥青混合料抗裂性能评价方法。确定沥青混合料配比参数,构建试件有限元计算模型,得到试件的CMOD曲线,将其与有限模型相结合,得到CMOD值;将相应的参数导入虚拟数字试验软件中,确定材料微观结构与力学性能之间的联系;根据沥青性能要求,设定实验环境参数以及抗裂性能评估指标,实现沥青混合料抗裂性能评价。构建仿真环节,实验结果证实,所提方法所得评价结果与实测结果基本一致,具有较高的可信度。

Modified Biphasic Mixture Model and Its Numerical Penalty Formulation

A new term involving the rate of pressure change is introduced into the continuity equation of an existing biphasic mixture model. Based on this new continuity equation, a penalized numerical formulation of finite element method is given. Computational result shows that this new biphasic mixture model can provide better description of the transient response of biological media such as articular cartilage, muscle, and soft tissue.

未知杂波环境下的多目标跟踪算法

提出了一种未知杂波环境下的多目标跟踪算法.该算法通过有限混合模型(Finite mixtrue model,FMM)建立多目标似然函数,其中混合模型参数可通过期望极大化(Expectation maximum,EM)算法及模型合并与删除技术得到.由估计的混合模型参数可进一步得到杂波模型估计、目标个数估计以及多目标状态估计.类似基于随机有限集(Random finite set,RFS)的多目标跟踪算法,该算法也可避免目标与测量的关联过程.仿真实验表明,当杂波分布未知并且较复杂时,本文算法的估计效果要明显优于未进行杂波拟合时的多目标跟踪算法.

一种快速、鲁棒的有限高斯混合模型聚类算法

有限混合模型聚类是一种基于概率模型的有效聚类方法。针对高斯混合模型的聚类算法,分别对模型的成分混合系数及样本所属成分的概率系数施加熵惩罚算子,实现对模型成分数的两级控制,快速消除无效成分,使算法能在很少的迭代次数内收敛到确定解。传统算法对初始值(成分数目c需事先指定)的设置非常敏感,容易导致EM算法陷入局部最优解或收敛到解空间的边界,而文中的算法对初始值的设定没有特殊的要求,实验证明其具有很好的鲁棒性。

覆盖算法的概率模型

要从本质上提高覆盖算法的精度,必须在算法中引入全局的优化计算.为此,先将覆盖算法扩展成核覆盖算法(以高斯函数为核函数),再利用高斯函数的概率意义(高斯分布),为核覆盖算法建立一个有限混合概率模型,在此基础上,利用"最大似然原理"引入全局优化计算,并利用EM(expectation maximization)方法进行求解,完成对覆盖算法的全局优化计算,从而扩大覆盖方法的使用范围并提高算法的精度,且将它从确定的模型扩展成概率的模型,后者更具抗噪声干扰的能力.最后给出模拟实验,实验比较结果表明,经优化后的概率模型确实提高了算法的精度.

长白山阔叶红松林径级模拟研究——林分模拟

该文利用指数分布、Weibull分布和混合分布3种类型7个方程模拟长白山阔叶红松林径级分布.研究结果表明,长白山阔叶红松林的径级分布不是理想的倒“J”型,基本为“S”型;用3个负指数方程和修正指数方程模拟均为倒“J”型,在半对数图上为直线;Weibull方程模拟出了单峰,但是效果一般;用2个和3个组分的Weibull混合模型对长白山阔叶红松林径级分布进行了成功模拟,3个组分的Weibull混合模型的模拟效果有所提高,但是并没有显著改善.

斜长石、辉石混合模型的电导率有限元数值计算研究

以岩石实验中矿物的几何形态及空间分布为建模依据,以实验条件及单矿物电导率的测量结果为约束条件,用有限元数值方法模拟了不同微观结构的斜长石、辉石混合物在施加电压后电势及电流的分布情况,并计算了混合模型在不同温度条件下的电导率.研究结果显示,数值模型网格数及矿物颗粒数的选取对电导率计算结果的精度有较大影响,在体导电情况下,模型电导率因矿物比例含量和排列结构而异.当斜长石及辉石随机分布时,随着辉石含量的增加,混合模型电导率在不同温度下均有所增加,且温度越高,增加幅度越大,电导率的有限元模拟计算结果接近于有效介质渗透理论模型,且位于并、串联模型之间以及HS模型的上、下边界范围内;在斜长石及辉石含量一定的情况下,各矿物的排列分布对电导率计算结果也有一定的影响,当矿物颗粒大小接近且分布均匀时,模型中电势沿电流传导方向变化较为均匀,模拟计算得出的电导率相对较高,当矿物颗粒大小差别较大及分布不均匀时,电势分布受到一定的扰动,电导率计算结果也较低.将混合模型电导率有限元计算结果与辉长岩、辉绿岩及玄武岩实验测量结果进行比较,显示这3种岩石样品电导率与温度变化关系的斜率均与混合模型计算结果的斜率相接近,表明这些岩石在所选温度段导电机制与斜长石、辉石混合模型相似,用斜长石、辉石混合模型的电导率研究玄武岩、辉长岩及辉绿岩的导电性具有适用性.将混合模型有限元计算结果与玄武岩、辉长岩、辉绿岩覆盖区地壳大地电磁实测结果对比,发现大地电磁电导率结果位于混合模型计算结果范围内,用斜长石、辉石混合模型模拟玄武岩、辉长岩等岩石地壳具有一定的可行性.

基于数字图像处理和有限元建模方法的沥青混合料劈裂试验数值模拟

应用数字图像处理技术及工业CT扫描获得试件图像,结合有限元建模方法,建立了包含集料、空隙和胶浆在内的沥青混合料有限元模型,并模拟研究了沥青混合料劈裂试验。结果表明:通过定义应力集中因子,可用来描述沥青混合料内部应力的不均匀分布,级配类型、模量比、有无空隙及加载位置都对模拟结果有较大影响。采用DIP-FEM方法能够很好地将沥青混合料的微观结构和宏观力学性能结合起来。