基于Koopman-Darmois分布族的序贯网图检验方法

通常高成本、破坏性的抽样检验需采用具有最大样本量限制的序贯检验方法．立足于设计出最大样本量尽量小的序贯检验方案,本文基于Koopman-Darmois分布族建立了序贯网图检验方法．与目前广泛采用的截尾序贯概率比检验方法相比,序贯网图检验方案具有更小的样本量上界,更适合高成本、破坏性的抽样检验．     

序贯Lq似然比型检验

本文研究了序贯Lq似然比型检验(简写为SLqRT),以及SLqRT的一些性质.基于其中一个性质-基本恒等式,得到SLqRT的势函数和平均子样容量.为了节约成本,通过最小化平均子样容量来选择合适的q值,从而进行指数分布的假设检验.此外,给出了理论推导及两个模拟算例来说明SLqRT的稳健性,并计算了不同污染参数下粗差模型的序贯概率比检验(简写为SPRT)和SLqRT的平均子样容量.结果表明:在平均子样容量下,SLqRT的效果优于SPRT.     

半正态分布参数的序贯概率比检验

研究半正态分布中参数的序贯概率比检验(记SPRT),主要目的是拓宽大学生的统计学知识和视野.首先,用SPRT法对该分布中参数作检验,得到停止法则;其次,根据SPRT的相关性质,得到半正态分布下SPRT的操作特性函数和平均样本容量;最后,在给定两个参数下分别计算SPRT方法和N-P检验法下所需的平均样本容量,前者所需的平均样本量大约是后者的35％-50％.     

越界概率与序贯似然比检验简介

一、引言二次大战时期,为了提高军火试验中抽样调查的效率,A.Wald等人首先较为系统地研究了序贯分析。Wald的奠基性著作问世以来,序贯分析的研究范围越来越大,理论和应用都有了很大的发展。尤其是在医学诊断中的应用有力地促进了序贯的理论研究。本文从一个侧面反映部分序贯分析的新动向。作重介绍从七十年代中期开始受到广泛注意的一种序贯似然比检验方法——重复显著性检验(Repeated Significance Test)。这种检验与在统计中得到广泛应用的越界概率(Boundary Crossing Probability)问题密切相关。本文试图总结有关重复显著性检验的最新成果;并扼要阐述以统计应用为目的的求越界概率的几种常用方法;我们还介绍一种与越界概率有关的统计模型——转折点(Change-Point)问题。1986年D.Siegmund发表于《Annals of Statistics》上的特邀论     

关于序贯检验的Bayes分析

本文将充分利用验前信息的Ｂａｙｅｓ方法与序贯检验相结合,推导出了Ｂａｙｅｓ序贯检验方法。文章从表面形式上的决策方案推导到实质上真正的决策方案;并对飞行器落点密集度进行了模拟计算的具体分析,最后得出结论,Ｂａｙｅｓ序贯检验方法对具有昂贵成本的产品试验和我国航天试验有较大的应用价值．     

参数模型下的时间序贯检验方案

本文研究参数模型下的序贯检验方案 .而以往的序贯检验方案往往采取非参数模型 .由于参数模型在生产实践中是常见的形式 .所以这个检验方案对于产品的检验具有指导意义 .     

序贯可加图的结构

给定一个(p,q)图G和一个正整数k，G的一个k序贯可加性编码是不同的数k,k+1,…,k+p+q-1到G的p+q个元素的一种分配，使得G的每一边e=uv得到分配给顶点u和v的数值之和。若图的元素容许有这样的一种分配，则称该图是一个k序贯可加图。该文将给出序贯可加图的若干结构性质，并构造一个k序贯可加图的无限簇。      

维修性验证中组合序贯试验方案的确定

本文给出了分布未知时两个百分位要求的组合序贯试验方案。     

卫星遥测数据的波动特征提取及应用

目前基于遥测数据的卫星在轨状态监测和异常检测,主要通过频谱分析等信号处理方法提取遥测特征,难以适应卫星遥测数据离散取值、数据量大、异常和噪声复杂等特点,所提取的特征量特点不突出,难以满足遥测数据异常检测要求.提出基于波动特征的卫星遥测数据特征提取方法,以遥测数据变化频数或累积变化次数作为卫星遥测数据特征,具有实现简单、快速高效、对异常数据不敏感等特点.基于所提取的波动特征,提出一种基于序贯概率比检验(SPRT)的卫星在轨异常检测方法.实例分析结果表明,所提取的特征量能够较好地识别卫星异常,具有较高的计算效率和较好的检测性能.     

DIASYS R/S 2003尿沉渣分析的截尾序贯检验

尿沉渣中红/白细胞的定量分析是尿常规检查中的重要检测指标,检查结果对肾和泌尿系统疾病诊断和鉴别诊断,病情严重程度,疗效观察和预后估计都有极其重要的价值.采用截尾序贯检验分析方法,对Diasys R/S 2003尿沉渣定量分析的传统计数方式进行了改进.计算机模拟结果表明,在假阳性率与假阴性率低于一定水平时,截尾序贯检验分析方法相比传统的检测方式极大地减少了尿沉渣检测的计数工作量.     

Method of sequential mesh on Koopman-Darmois distributions

For costly and/or destructive tests,the sequential method with a proper maximum sample size is needed.Based on Koopman-Darmois distributions,this paper proposes the method of sequential mesh,which has an acceptable maximum sample size.In comparison with the popular truncated sequential probability ratio test,our method has the advantage of a smaller maximum sample size and is especially applicable for costly and/or destructive tests.     

Parallel anisotropic mesh adaptivity with dynamic load balancing for cardiac electrophysiology

Simulations in cardiac electrophysiology generally use very fine meshes and small time steps to resolve highly localized wavefronts. This expense motivates the use of mesh adaptivity, which has been demonstrated to reduce the overall computational load. However, even with mesh adaptivity performing such simulations on a single processor is infeasible. Therefore, the adaptivity algorithm must be parallelised. Rather than modifying the sequential adaptive algorithm, the parallel mesh adaptivity method introduced in this paper focuses on dynamic load balancing in response to the local refinement and coarsening of the mesh. In essence, the mesh partition boundary is perturbed away from mesh regions of high relative error, while also balancing the computational load across processes. The parallel scaling of the method when applied to physiologically realistic heart meshes is shown to be good as long as there are enough mesh nodes to distribute over the available parallel processes. It is shown that the new method is dominated by the cost of the sequential adaptive mesh procedure and that the parallel overhead of inter-process data migration represents only a small fraction of the overall cost.     

A reduced domain strategy for local mesh movement application in unstructured grids

Automatic control of mesh movement is mandatory in many fluid flow and fluid-solid interaction problems. This paper presents a new strategy, called reduced domain strategy (RDS), which enhances the efficiency of node connectivity-based mesh movement methods and moves the unstructured grid locally and effectively. The strategy dramatically reduces the grid computations by dividing the unstructured grid into two active and inactive zones. After any local boundary movement, the grid movement is performed only within the active zone. To enhance the efficiency of our strategy, we also develop an automatic mesh partitioning scheme. This scheme benefits from a new quasi-structured mesh data ordering, which determines the boundary of active zone in the original unstructured grid very easily. Indeed, the new partitioning scheme eliminates the need for sequential reordering of the original unstructured grid data in different mesh movement applications. We choose the spring analogy method and apply our new strategy to perform local mesh movements in two boundary movement problems including a multi-element airfoil with moving slat or deforming main body section. We show that the RDS is robust and cost effective. It can be readily employed in different node connectivity-based mesh movement methods. Indeed, the RDS provides a flexible local grid deformation tool for moving grid applications.     

Parallel collocation solution of index-1 BVP-DAEs arising from constrained optimal control problems

The indirect solution of constrained optimal control problems gives rise to two-point boundary value problems (BVPs) that involve index-1 differential-algebraic equations (DAEs) and inequality constraints. This paper presents a parallel collocation algorithm for the solution of these inequality constrained index-1 BVP-DAEs. The numerical algorithm is based on approximating the DAEs using piecewise polynomials on a nonuniform mesh. The collocation method is realized by requiring that the BVP-DAE be satisfied at Lobatto points within each interval of the mesh. A Newton interior-point method is used to solve the collocation equations, and maintain feasibility of the inequality constraints. The implementation of the algorithm involves: (i) parallel evaluation of the collocation equations; (ii) parallel evaluation of the system Jacobian; and (iii) parallel solution of a boarded almost block diagonal (BABD) system to obtain the Newton search direction. Numerical examples show that the parallel implementation provides significant speedup when compared to a sequential version of the algorithm.     

A higher order finite element method with modified graded mesh for singularly perturbed two-parameter problems

This paper presents a modified graded mesh for singularly perturbed two-parameter problems. The mesh is generated recursively using Newton's algorithm and some implicitly defined function. The problem is solved numerically using the finite element method based on higher order polynomials of degree p≥1. We prove parameter uniform convergence of optimal order in ε-weighted energy norm. A test example is taken to compare the proposed graded mesh with others found in the literature.     

A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems

A coupled system of two singularly perturbed linear reaction–diffusiontwo-point boundary value problems is examined. The leading termof each equation is multiplied by a small positive parameter,but these parameters may have different magnitudes. The solutionsto the system have boundary layers that overlap and interact.The structure of these layers is analysed, and this leads tothe construction of a piecewise-uniform mesh that is a variantof the usual Shishkin mesh. On this mesh central differencingis proved to be almost first-order accurate, uniformly in bothsmall parameters. Supporting numerical results are presentedfor a test problem.     

A self-adaptive moving mesh method for the Camassa-Holm equation

A self-adaptive moving mesh method is proposed for the numerical simulations of the Camassa-Holm equation. It is an integrable scheme in the sense that it possesses the exact N-soliton solution. It is named a self-adaptive moving mesh method, because the non-uniform mesh is driven and adapted automatically by the solution. Once the non-uniform mesh is evolved, the solution is determined by solving a tridiagonal linear system. Due to these two superior features of the method, several test problems give very satisfactory results even if by using a small number of grid points.     

Experimental Study on the Flexural Ductility of BFRP Bar Concrete Beams With Bamboo Fiber and Steel Wire Mesh北大核心CSCD

To study the effects of bamboo fiber and steel wire mesh on the flexural ductility of basalt fiber reinforced polymer（BFRP）bar concrete beams, 7 BFRP bar concrete beams with bamboo fiber and steel wire mesh were tested with different bamboo fiber lengths (0 mm, 30 mm and 45 mm) and different steel wire mesh layout ranges (0, 1/2 maximum bending moment point layout and full beam length layout). The flexural failure tests of the 7 beams were carried out, and the initial crack loads, the crack developments, the ultimate loads and the deformations were detected. The effects of the fiber length and the wire mesh layout range on the crack resistance and the deformation resistance of the specimens were analyzed based on the test data. With the function model, the equivalent yield points of the 7 test beams were obtained, and their ductility coefficients were calculated. The results show that, the addition of bamboo fiber and steel wire mesh increases the cracking loads of BFRP bar concrete beams by 12%~68%, decreases the crack spacings and the crack length development speed, reduces the test beam deformation under the same load, and increases the ductility coefficient by 1.58%~31.75%. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Truncated Sequential Test for a Proportion and it's Sample Space Ordering Method

This paper proposes a new sampling plan, the sample space ordering method, to compute the optimum truncated sequential test in order to overcome the disadvantages of the widely use sequential sampling methods that IEC1123 has presented. The main ideal of this new method is to establish an order at the truncated sequential sample space, and optimize point by point to arrive the optimal truncated sequential test. The paper presents in detail how to realize the new plan, and shows that this new plan has most powerful to control the sample number and least average sample number comparing with the methods which IEC1123 and SMT have proposed.     

The Generalized Patch Test for Zienkiewicz's Triangles

It is proved that Zienkiewicz's triangles for plate bending problems pass Stummel's generalized patch test — a necessary and sufficient condition for convergence of nonconforming finite elements — for mesh (a) generated by three sets of parallel lines, but do not pass it when "union jack" mesh (b) or when another mesh (c) is used. In the latter two cases the approximations are divergent.