A general result on precise asymptotics for linear processes of positively associated sequences

Let {εt; t ∈ Z^＋} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2＋1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^＋} is a sequence of real numbers satisfying ∑j=0^∞｜aj｜〈∞.Define a linear process Xt=∑j=0^∞ ajεt-j,t≥1,and Sn=∑t=1^n Xt,n≥1.Assume that E｜ε1｜^2＋δ′〈 for some δ′〉0 and μ（n）=O（n^-ρ） for some ρ〉0.This paper achieves a general law of precise asymptotics for {Sn}.

Central limit theolrem for linear processes generated byⅡD random variables under the sub-linear expectation

In this paper,we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed(IID)random variables for sub-linear expectations initiated by Peng[19].It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's central limit theorem and invariance principle to the case where probability measures are no longer additive.

The SCUSUM Estimation of Variance Change Point in Linear Process

这份报纸在线性过程考虑一个变化变化点的评价问题。一个 SCUSUM 类型变化点评估者的一致性被证明，它集中的率被建立。平均数未知的盒子也被考虑。

ε-arithmetics for real vectors and linear processing of real vector-valued signals

In this paper,we introduce a new concept,namelyε-arithmetics,for real vectors of any fixed dimension.The basic idea is to use vectors of rational values(called rational vectors)to approximate vectors of real values of the same dimension withinεrange.For rational vectors of a fixed dimension m,they can form a field that is an mth order extension Q(α)of the rational field Q whereαhas its minimal polynomial of degree m over Q.Then,the arithmetics,such as addition,subtraction,multiplication,and division,of real vectors can be defined by using that of their approximated rational vectors withinεrange.We also define complex conjugate of a real vector and then inner product and convolutions of two real vectors and two real vector sequences(signals)of finite length.With these newly defined concepts for real vectors,linear processing,such as linear filtering,ARMA modeling,and least squares fitting,can be implemented to real vectorvalued signals with real vector-valued coefficients,which will broaden the existing linear processing to scalar-valued signals.

The Invariance Principle for Linear Processes Generated by a Negatively Associated Sequence and Its Applications

Abstract In this paper, we obtain the invariance principle for linear processes generated by a negativelyassociated sequence.

Imperfect preventive maintenance for numerical control machine tools with log-linear virtual age process

Based on the log-linear virtual age process, an imperfect preventive maintenance policy for numerical control(NC)machine tools with random maintenance quality is proposed. The proposed model is a combination of the Kijima type virtual age model and the failure intensity adjustment model. Maintenance intervals of the proposed hybrid model are derived when the failure intensity increase factor and the restoration factor are both random variables with uniform distribution. The optimal maintenance policy in infinite time horizon is presented. A numerical example is given when the failures of NC machine tools are described by the log-linear process. Finally, a discussion is presented to show how the optimal results depend on the different cost parameters.

Complete Moment Convergence for the Dependent Linear Processes with Random Coefficients

In this paper, we investigate the complete moment convergence for dependent linear processes with random coefficients to form Xt =∑j^∞=∞ Aj∈t-j,where {∈n, n ∈ Z} is a sequence of END stochastically dominated random variables and {An,n ∈ Z} is a sequence of random varibles. As applications, the convergence rate, Marcinkiewicz-Zvgmund strong law and strong law of large numbers for this linear process are established.

Optimal Iterative Learning Control for Batch Processes Based on Linear Time-varying Perturbation Model

为在批的产品质量的追踪的控制的最佳的反复的学习控制(ILC ) 策略处理的 batch-to-batch 被介绍。线性变化时间的不安(LTVP ) 模型在名字的轨道附近为产品质量被造。到模型植物失配的地址问题，在以前的成批处理的模型预言错误为当前的成批处理被加到模型预言。然后追踪错误转变模型能被造，并且有直接错误反馈的 ILC 法律明确地被获得。一条严密定理被建议，到证明在 ILC 下面追踪错误的集中。建议方法论在一个典型的批反应堆和轨道追踪的表演被 ILC 逐渐地改进的结果表演上被说明。

Image Processing System for Air Classification Using Linear Discriminant Analysis

An air classifier is used in the recycling process of covered electric wire in the recycling factories, in which the covered electric wires are crushed, sieved, and classified by the air classifier, which generates wastes. In these factories, operators manually adjust the air flow rate while checking the wastes discharged from the separator outlet. However, the adjustments are basically done by trial and error, and it is difficult to do them appropriately. In this study, we tried to develop the image processing system that calculates the ratio of copper (Cu) product and polyvinyl chloride (PVC) in the wastes as a substitute for the operator’s eyes. Six colors of PVC (white, gray, green, blue, black, and red) were used in the present work. An image consists of foreground and background. An image’s regions of interest are objects (Cu particles) in its foreground. However, the particles having a color similar to the background color are buried in the background. Using the difference of two color backgrounds, we separated particles and background without dependent of background. The Otsu’ thresholding was employed to choose the threshold to maximize the degree of separation of the particles and background. The ratio of Cu to PVC pixels from mixed image was calculated by linear discriminant analysis. The error of PVC pixels resulted in zero, whereas the error of Cu pixels arose to 4.19%. Comparing the numbers of Cu and PVC pixels within the contour, the minority of the object were corrected to the majority of the object. The error of Cu pixels discriminated as PVC incorrectly became zero percent through this correction.

THE MONITORING FOR PHYSICAL DEVELOPING PROCESS WITH A LINEAR CCD

In this work, we used a linear CCD to detect the whole physical developing process of silver diffusion transfer reversal process in photographic chemistry. The influence of the ingredient of the working solution was studied.

Some Applications of Higher Moments of the Linear Gaussian White Noise Process

The Linear Gaussian white noise process is an independent and identically distributed (iid) sequence with zero mean and finite variance with distribution N (0, σ2 ) . Hence, if X1, x2, …, Xn is a realization of such an iid sequence, this paper studies in detail the covariance structure of X1d, X2d, …, Xnd, d=1, 2, …. By this study, it is shown that: 1) all powers of a Linear Gaussian White Noise Process are iid but, not normally distributed and 2) the higher moments (variance and kurtosis) of Xtd, d=2, 3, … can be used to distinguish between the Linear Gaussian white noise process and other processes with similar covariance structure.

DATA PROCESSING ON LINEARIZATION OF HOT-WIRE ANEMOMETER

A method of data processing to determine the coefficients of linearization equations for 1050 anemometer (produced by Thermo-Systems Inc. -TSI, USA) with the sensors made of domestic hot wire using the program preferred in this Paper is described. By calculation and test, it is indicated that the error resulting from this method is about 0. 5% of the full scale and less than TSl's. By using this method we can set up the calibration curve according to the measurement range and the diameter of the hot wire at a certain accuracy.

Evaluating Traffic Congestion Using the Traffic Occupancy and Speed Distribution Relationship: An Application of Bayesian Dirichlet Process Mixtures of Generalized Linear Model

Accurate classification and prediction of future traffic conditions are essential for developing effective strategies for congestion mitigation on the highway systems. Speed distribution is one of the traffic stream parameters, which has been used to quantify the traffic conditions. Previous studies have shown that multi-modal probability distribution of speeds gives excellent results when simultaneously evaluating congested and free-flow traffic conditions. However, most of these previous analytical studies do not incorporate the influencing factors in characterizing these conditions. This study evaluates the impact of traffic occupancy on the multi-state speed distribution using the Bayesian Dirichlet Process Mixtures of Generalized Linear Models (DPM-GLM). Further, the study estimates the speed cut-point values of traffic states, which separate them into homogeneous groups using Bayesian change-point detection (BCD) technique. The study used 2015 archived one-year traffic data collected on Florida’s Interstate 295 freeway corridor. Information criteria results revealed three traffic states, which were identified as free-flow, transitional flow condition (congestion onset/offset), and the congested condition. The findings of the DPM-GLM indicated that in all estimated states, the traffic speed decreases when traffic occupancy increases. Comparison of the influence of traffic occupancy between traffic states showed that traffic occupancy has more impact on the free-flow and the congested state than on the transitional flow condition. With respect to estimating the threshold speed value, the results of the BCD model revealed promising findings in characterizing levels of traffic congestion.

Decomposition of Supercritical Linear-Fractional Branching Processes

It is well known that a supercritical single-type Bienayme-Galton-Watson process can be viewed as a decomposable branching process formed by two subtypes of particles: those having infinite line of descent and those who have finite number of descendants. In this paper we analyze such a decomposition for the linear-fractional Bienayme-Galton-Watson processes with countably many types. We find explicit expressions for the main characteristics of the reproduction laws for so-called skeleton and doomed particles.

Application of Dynamic Linear Detecting Method in Data Processing of the Portable Blood Sugar Analyzer

In this paper,a dynamic linear detecting method,that the non-linear coefficient NL% was led and the non-linearity of data were estimated continuously and dynamically and determined when NL% exceeded reference value (5%),was used for data processing and could solve the problem caused by the phenomenon of substrate depleting occurred following the redox reaction in portable blood sugar analyzer.By contrast to the conventional end-point method,the dynamic linear detecting method is based on multipoint data collecting.Experiments of measuring the calibration glucose solution with 8 various concentrations from 50 mg/dl to 400 mg/dl were carried out with the analyzer developed by our group.The linear regression curve,whose correlation for the data was 0.9995 and the residual was 2.8080,were obtained.The obtained correlation,residual, and the computation workload are all fit for the portable blood sugar analyzer.

基于图像处理的水培生菜冠层图像叶面积估测研究

为实现精准、高效、无损地获取植物工厂环境下水培生菜相关长势参数叶面积(Leaf area,LA),基于数字图像处理和机器学习回归方法建立单株水培生菜冠层图像LA估测模型。首先,通过智能手机获取2个生菜品种不同生长期的冠层可见光图像,利用Photoshop图像处理软件将原始图像统一剪裁为900像素×900像素大小,采用中值滤波(MedianBlur)法对剪裁后的图像进行去噪运算,将RGB图像转化为HSV颜色空间,再采用mask掩膜法分割彩色图像;然后,利用图像法获取单株生菜LA实测值,构建以LA实测值为因变量,以生菜冠层投影面积(Projected leaf area,PLA)为自变量的线性回归(Linear regression,LR)模型和以全局图像特征(颜色、形状、纹理等)为自变量的支持向量回归(Support vector regression,SVR)、多元线性回归(Multiple linear regression,MLR)和随机森林(Random forest,RF)等LA估测模型进行对比分析;最后,采用决定系数(Coefficient of determination,R^(2))和均方根误差(Root mean square error,RMSE)评估模型的准确性。结果表明:RF模型估测效果最好,对于生菜品种‘绿萝’单株LA估测结果的R^(2)为0.9714、RMSE为8.89 cm2,对于品种‘碧霄’估测结果的R^(2)为0.9201、RMSE为23.34 cm2。本研究验证了RF回归模型能够较准确地估测生菜单株叶面积,可为植物工厂水培生菜LA无损估测提供新的解决方案和研究基础。

STRONG APPROXIMATION FOR MOVING AVERAGE PROCESSES UNDER DEPENDENCE ASSUMPTIONS

Let {Xt,t ≥ 1} be a moving average process defined by Xt = ∑^∞ k=0 αkξt-k, where {αk,k ≥ 0} is a sequence of real numbers and {ξt,-∞ 〈 t 〈 ∞} is a doubly infinite sequence of strictly stationary dependent random variables. Under the conditions of {αk, k ≥ 0} which entail that {Xt, t ≥ 1} is either a long memory process or a linear process, the strong approximation of {Xt, t ≥ 1} to a Gaussian process is studied. Finally, the results are applied to obtain the strong approximation of a long memory process to a fractional Brownian motion and the laws of the iterated logarithm for moving average processes.

Processing Modflow模型在预测地面沉降中的应用

研究目的:针对开采地下水引起的区域地面沉降对线性工程的影响问题,以京津城际铁路为例,采用地下水三维渗流与地面沉降耦合模型计算软件—Processing Modflow,选择沿线地面沉降较严重区段,建立区域地下水流场与地面沉降的耦合模型,运用参数修正后的模型,进行地面沉降预测。研究结论:利用实测地面沉降值对模型进行验证,沉降中心位置及沉降量的模拟结果与实测结果基本吻合;设计不同的地下水开采方案,利用模型预测地面沉降,结果表明:合理压采地下水可以降低地面沉降量及沉降坡度,减缓地面沉降的不均匀性。

基于线性规划优化小精细化工企业的生产措施

由于小精细化工企业生产灵活、工艺复杂、对成本和利润控制严格,因此,对生产工艺的优化,就成为小精细化工企业生产措施改进的主要内容之一。文章结合小精细化工企业的生产状况以及在该状况条件下相应的约束因素等,采用运筹学线性规划法构建最优计划数学模型,利用计算软件就具体数据进行求解,得到生产计划的最优解。