基于自适应多保真度Co-Kriging代理模型的地下水污染源反演识别

为高效率高精度地进行地下水污染源反演识别,综合运用高保真度和低保真度地下水溶质运移数值模拟模型,研究应用集成差分进化算法的Co-Kriging方法建立模拟模型的多保真度代理模型;在此基础上,探索应用马尔科夫链蒙特卡洛(MCMC)-DREAM_((D))算法,并采用自适应更新多保真度代理模型策略进行地下水污染源反演识别.为验证上述方法的有效性和可行性,开展了数值算例研究.结果表明:相比仅基于高保真度模型输入-输出样本构建的Kriging代理模型,联合运用高保真度和低保真度模型输入-输出样本构建的Co-Kriging代理模型对模拟模型的逼近精度更高;耦合多保真度Co-Kriging代理模型和MCMC-DREAM_((D))算法能够得到较高精度的污染源反演结果,且能够大幅度减小计算负荷;同时,采用自适应更新多保真度代理模型策略能够进一步提高污染源反演识别精度.

Review of Collocation Methods and Applications in Solving Science and Engineering Problems

The collocation method is a widely used numerical method for science and engineering problems governed by partial differential equations.This paper provides a comprehensive review of collocation methods and their applications,focused on elasticity,heat conduction,electromagnetic field analysis,and fluid dynamics.The merits of the collocation method can be attributed to the need for element mesh,simple implementation,high computational efficiency,and ease in handling irregular domain problems since the collocation method is a type of node-based numerical method.Beginning with the fundamental principles of the collocation method,the discretization process in the continuous domain is elucidated,and how the collocation method approximation solutions for solving differential equations are explained.Delving into the historical development of the collocation methods,their earliest applications and key milestones are traced,thereby demonstrating their evolution within the realm of numerical computation.The mathematical foundations of collocation methods,encompassing the selection of interpolation functions,definition of weighting functions,and derivation of integration rules,are examined in detail,emphasizing their significance in comprehending the method’s effectiveness and stability.At last,the practical application of the collocation methods in engineering contexts is emphasized,including heat conduction simulations,electromagnetic coupled field analysis,and fluid dynamics simulations.These specific case studies can underscore collocation method’s broad applicability and effectiveness in addressing complex engineering challenges.In conclusion,this paper puts forward the future development trend of the collocation method through rigorous analysis and discussion,thereby facilitating further advancements in research and practical applications within these fields.

A Collocation Technique via Pell-Lucas Polynomials to Solve Fractional Differential EquationModel for HIV/AIDS with Treatment Compartment

In this study,a numerical method based on the Pell-Lucas polynomials(PLPs)is developed to solve the fractional order HIV/AIDS epidemic model with a treatment compartment.The HIV/AIDS mathematical model with a treatment compartment is divided into five classes,namely,susceptible patients(S),HIV-positive individuals(I),individuals with full-blown AIDS but not receiving ARV treatment(A),individuals being treated(T),and individuals who have changed their sexual habits sufficiently(R).According to the method,by utilizing the PLPs and the collocation points,we convert the fractional order HIV/AIDS epidemic model with a treatment compartment into a nonlinear system of the algebraic equations.Also,the error analysis is presented for the Pell-Lucas approximation method.The aim of this study is to observe the behavior of five populations after 200 days when drug treatment is applied to HIV-infectious and full-blown AIDS people.To demonstrate the usefulness of this method,the applications are made on the numerical example with the help of MATLAB.In addition,four cases of the fractional order derivative(p=1,p=0.95,p=0.9,p=0.85)are examined in the range[0,200].Owing to applications,we figured out that the outcomes have quite decent errors.Also,we understand that the errors decrease when the value of N increases.The figures in this study are created in MATLAB.The outcomes indicate that the presented method is reasonably sufficient and correct.

Effects of Collocational Congruency,Frequency and L2 Proficiency on the Processing of English Adjective-Noun Collocations

The present study investigates the effects of congruency and frequency on adjective-noun collocational processing for Chinese learners of English at two proficiency levels based on the data obtained in an online acceptability judgment task.The subject pool of this research included 60 English majors studying at a university in China;30 were selected as a higher-proficiency group and 30 as a lower-proficiency group according to their Vocabulary Levels Test(Schmitt et al.,2001)scores and their self-reported proficiency in English.The experimental materials were programmed to E-prime 2.0 and included six types of collocations:(1)15 high-frequency congruent collocations,(2)15 low-frequency congruent collocations,(3)15 high-frequency incongruent collocations,(4)15 low-frequency incongruent collocations,(5)15 Chinese-only items,and(6)75 unrelated items for baseline data.The collected response times(RTs)and accuracy rates data were statistically analyzed by the use of an ANOVA test and pairwise comparisons through SPSS 16.0 software.The results revealed that:(1)the adjective-noun collocational processing of Chinese English learners is influenced by collocational frequency,congruency and L2 proficiency;(2)the processing time is affected by the interaction of congruency and frequency;and(3)the interactive effect of L2 proficiency in conjunction with congruency and frequency also influences the processing quality.

贝叶斯同位置协同克里金(Bayesian collocated CoKriging)估值法的研究

针对原同位置协同克里金 (CollocatedCoKriging)法在研究区域大、硬数据少、择优采样严重的情况下 ,外推不可靠和贝叶斯克里金 (BayesianKriging)法在估计先验数据期望值时对尺度敏感的问题 ,根据这两种方法的原理提出并推导一种新的贝叶斯同位置协同克里金估值方法 .论述了该方法不但具有一般克里金法的性质 ,而且综合了前两种方法的优点 .通过实例验证 ,其估值效果良好 .

Antenna selection in MIMO radar with collocated antennas

An antenna adjustment strategy is developed for the target tracking problem in the collocated multiple-input multipleoutput(MIMO)radar.The basic technique of this strategy is to optimally allocate antennas by the prior information in the tracking recursive period,with the objective of enhancing the worst-case estimate precision of multiple targets.On account of the posterior Cramer-Rao lower bound(PCRLB)offering a quantitative measure for target tracking accuracy,the PCRLB of joint direction-of-arrival(DOA)and Doppler is derived and utilized as the optimization criterion.It is shown that the dynamic antenna selection problem is NP-hard,and an efficient technique which combines convex relaxation with local search is put forward as the solution.Simulation results demonstrate the outperformance of the proposed strategy to the fixed antenna configuration and heuristic search algorithm.Moreover,it is able to offer close-to performance of the exhaustive search method.

Adaptive time-space resource and waveform control for collocated MIMO radar with simultaneous multi-beam

Collocated multiple input multiple output(MIMO)radar,which has agile multi-beam working mode,can offer enhanced multiple targets tracking(MTT)ability.In detail,it can illuminate different targets simultaneously with multi-beam or one wide beam among multi-beam,providing greater degree of freedom in system resource control.An adaptive time-space resource and waveform control optimization model for the collocated MIMO radar with simultaneous multi-beam is proposed in this paper.The aim of the proposed scheme is to improve the overall tracking accuracy and meanwhile minimize the resource consumption under the guarantee of effective targets detection.A resource and waveform control algorithm which integrates the genetic algorithm(GA)is proposed to solve the optimization problem.The optimal transmitting waveform parameters,system sampling period,sub-array number,binary radar tracking parameterχ_i(t_k),transmitting energy and multi-beam direction vector combination are chosen adaptively,where the first one realizes the waveform control and the latter five realize the timespace resource allocation.Simulation results demonstrate the effectiveness of the proposed control method.

A Numerical Investigation Based on Exponential Collocation Method for Nonlinear SITR Model of COVID-19

In this work,the exponential approximation is used for the numerical simulation of a nonlinear SITR model as a system of differential equations that shows the dynamics of the new coronavirus(COVID-19).The SITR mathematical model is divided into four classes using fractal parameters for COVID-19 dynamics,namely,susceptible(S),infected(I),treatment(T),and recovered(R).The main idea of the presented method is based on the matrix representations of the exponential functions and their derivatives using collocation points.To indicate the usefulness of this method,we employ it in some cases.For error analysis of the method,the residual of the solutions is reviewed.The reported examples show that the method is reasonably efficient and accurate.

On the Mathematical Model of Universal Co-kriging

Due to its complexities in both mathematicM formulations and applications, universal co-kriging （UCK） has not been sufficiently discussed in literature. An extended and simpler matrix formulation UCK with incorporation of a polynomial variable trend is proposed in this paper. Estimators of the value and expectation of a regionMized vector taken in a point are obtained on the basis of cross-covaxiance and cross-vaxiogram, respectively. The complex expressions of co-kriging with trend are greatly simplified by introducing special matrix operations, such as Kronecker product, into the formulations. This simplification offers a feasible and easier approach for computer coding of the UCK, and helps the practitioners to use the UCK technique conveniently in real cases.

基于Triple-Collocation多源地表温度数据融合方法研究

为充分利用多源地表温度数据,提高区域尺度下地表温度精度,改善地表温度遥感产品的适用性。以淮河流域为研究区,Triple-Collocation(TC)方法为基础,采用最小二乘法,由中分辨率光谱成像仪(MODIS)地表温度与风云三号可见光红外扫描辐射计(FY-3C/VIRR)地表温度遥感产品,结合地面观测站实测数据,研究多源数据融合方法。将淮河流域39个气象站点分为融合站点与验证站点,由融合站点采用反距离插值(IDW)算法得到区域连续地表温度数据,与FY-3C/VIRR地表温度数据、MODIS地表温度数据,融合得到淮河流域地表温度。与地面验证站点对比分析表明,融合后的地表温度,其R^(2)、RMSE和MAE分别为0.98、1.10 K、0.88 K,优于MODIS地表温度的0.92、2.59 K、2.18 K和FY-3C地表温度产品的0.84、6.68 K、5.35 K,精度得到了显著的提高。淮河流域不同月份的温度变化季节性规律明显,且变化主要出现在中部及东部地区,最高温度变化值都达到了20 K以上。

BITS: an efficient transport solver based on a collocation method with B-spline basis

A B-spline Interpolation Transport Solver(BITS) based on a collocation method is developed. It solves transport equations as a generalized interpolation problem, taking the first-order accuracy in time and the second-order accuracy in space along with a predictor–corrector or under-relaxation iteration method. Numerical tests show that BITS can solve one-dimensional transport equations for tokamak plasma more accurately without additional computation cost, compared to the finite difference method transport solver which is widely used in existing tokamak transport codes.

基于Co-Kriging代理模型的扇形冷却孔结构优化

为进一步提高航空发动机的冷却效率,对扇形气膜冷却孔进行优化研究,优化参数为直孔段孔长L,前向扩展角α和后向扩展角β,优化目标为气膜孔下游内平均气膜冷却效率。首先对优化变量进行拉丁超立方采样,然后对疏、密两种质量的网格进行有限元分析,得到两种可信度数据,进而构建Co-Kriging代理模型,最后引入遗传算法进行全局寻优,寻找最优的扇形孔结构。在吹风比为1.5的工况下,优化后的直孔段孔长、前向扩展角和后向扩展角分别为2.6D、41°、14°,冷却效率提升了45%。研究结果表明,较小的直孔段和较大的后向扩展角可以有效地抑制肾型涡对的产生,气膜冷却效果更好。

Finite Element Orthogonal Collocation Approach for Time Fractional Telegraph Equation with Mamadu-Njoseh Polynomials

Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a variational form over a given space, say a Hilbert space, are better numerically handled with the FEM. The FEM algorithm is used in various applications which includes fluid flow, heat transfer, acoustics, structural mechanics and dynamics, electric and magnetic field, etc. Thus, in this paper, the Finite Element Orthogonal Collocation Approach (FEOCA) is established for the approximate solution of Time Fractional Telegraph Equation (TFTE) with Mamadu-Njoseh polynomials as grid points corresponding to new basis functions constructed in the finite element space. The FEOCA is an elegant mixture of the Finite Element Method (FEM) and the Orthogonal Collocation Method (OCM). Two numerical examples are experimented on to verify the accuracy and rate of convergence of the method as compared with the theoretical results, and other methods in literature.

A Comparative Study on Verb-Noun Collocation Errors of Chinese EFL Learners with Different Language Proficiency

This study presents a comparative analysis of verb-noun collocation errors made by Chinese EFL learners with different language proficiency.Linguistic data from two sub-corpora of CLEC(Chinese Learner English Corpus,Gui&Yang,1999)consist of the compositions written freely by Chinese senior high school students(ST2)and the 3rd-and 4th-year English majors of Chinese universities(ST6).The study results show that four types of verb-noun collocation errors are frequently made due to incorrect L1 translation,misuse of relative synonyms,misuse of delexical verbs,and misuse of part of speech;the number of errors decreases with the development of language proficiency,especially errors by incorrect L1 translation and relative synonyms.And for both ST2 and ST6 EFL learners,errors resulted from incorrect L1 translation account for nearly a half with the same high-frequency words.It is also found that ST6 learners’competence in collocation and synonym identification doesn’t grow with the increase of their vocabulary,as is shown in the case of overusing delexical verbs in collocation,the same error made by ST2 learners,who have a significantly weaker command of delexical verbs.Implications of the findings are also discussed with the purpose of raising the awareness of collocation pedagogy and enhancing EFL learners’collocation competence.

广义弱形式自由单元法

自由单元法(FrEM)是一种单元配点法,吸收了有限元法等参单元的插值稳定性与无网格法使用灵活的优点,具有稳定性好和灵活性高的性能.FrEM在每个配置点只需要一个通过自由选择周围节点而形成的独立的等参单元,不需要考虑单元之间节点的相互连接关系,这种自由性使得人们可以按照学科性质形成所需要的单元,因而FrEM既适用于固体力学,也适用于流体力学问题的求解.然而,FrEM所用单元需要至少有一个内部节点(用于方程的配点),以致有限元法中单元节点相连的网格不能在FrEM中直接使用.文章基于对应于配置点的等参单元形函数在与其不相连的边界上为0的特性和配置点等效节点力平衡关系,提出了一种广义弱形式自由单元法(GFrEM).该方法是一种使用单元逐点建立配置方程的单元配点法,具有如下特点:(1)突破了现有自由单元法中单元需要内部节点的限制,因而可以使用线性单元和高阶单元;(2)突破了现有自由单元法中一个配置点使用一个单元的限制,可以使用与配置点相连的任意多个单元;(3)可以使用任意形式的规则单元和多边形/多面体单元;(4)如果使用单元节点相连的传统有限元法网格,则GFrEM自然演变为传统的有限元法.论文将给出几个固体力学方面的应用算例,展示所提方法的有效性.

对积极老龄化的“积极”意义的建构研究

采用语料库语言学的研究方法,以我国主流媒体的“老龄化”新闻为语料,对节点词“老年人”和“积极”的搭配词和搭配网络进行数据分析和文本解读,旨在深入探究我国主流媒体对积极老龄化国家战略中“积极”意义的构建特征和局限性。研究发现,“积极”具有与时俱进性、梯次性和系统性,同时指出“积极”意义在老年人照顾家人的经济价值、老年教育的内容涵盖范围以及老龄化社会建设的参与主体范围三个方面存在局限性。

非圆形隧洞衬砌支护下应力与位移的新解法

以往在利用平面弹性复变函数方法进行衬砌支护作用下非圆形隧洞的力学分析时,一般将洞室外域保角映射到象平面的单位圆外域,并认为可以利用同一个映射函数将衬砌截面映射到象平面的圆环域内。当衬砌厚度很薄时,这种方法是可行的,而当衬砌相对较厚时,利用同一映射函数所得到的衬砌截面形状发生严重失真。为解决此问题,本文引入两套映射函数,分别将洞室外域映射到象平面的单位圆的圆外域,衬砌截面映射到圆环域。这种方法可以适应于不同的衬砌厚度,利用这种方式获得的衬砌截面,在衬砌较厚时仍能保证衬砌厚度相对均匀。在求解解析函数过程中不再采用传统的幂级数解法,而是使用边界配点法,将两套映射函数结合,获得了该问题的应力解和位移解。本文以马蹄形隧洞为例,求解结果与ANSYS软件所得数值解吻合很好,分析了衬砌厚度对隧洞应力和位移的影响。根据本文解答可以方便、快捷地进行相近条件下隧道的初步设计。

同译同形性对韩国留学生汉语三字组合加工的影响

同译性,即词语搭配在母语和目的语中的翻译具有一致性,对二语词汇加工的影响已经在多种不同语言的习得中得到验证。但是,当母语和目的语同属汉字文化圈时,在翻译同译性的基础上词语之间还存在是否同形的差异。本文通过词汇判断实验,考察在具备同译性条件下,同形性对韩国留学生汉语三字组合加工的影响。结果显示,同译同形性对三字组合加工有影响,具体表现为同译同形组的反应时比同译不同形组更短,二者差异达到显著水平。本研究支持双语词汇通达的非选择性激活。

汉语框架语义网中词元语义搭配模式确定规则研究

机器理解自然语言和抽取信息涉及对词汇语义信息和句法信息两项重要内容的理解。汉语框架语义知识库(CFN)的词元语义搭配模式记录了词元与框架元素、词元与句法的组合方式,为机器自动进行语义分析和信息抽取提供了资源。而目前的词元语义搭配模式的数量多,机器确定并应用词元语义搭配模式存在一定困难,且框架元素间的关系比较模糊,词元配价成分的语义信息存在歧义,使机器不能准确理解和抽取文本信息。采用基于规则的方法,根据词元配价成分的语义信息和语义特征、词元外部的语境和框架元素提炼规则,可以使机器能够更准确地理解与抽取文本的语义信息。

基于Triple Collocation方法的土壤湿度误差分析

土壤湿度作为水循环中重要的驱动参数之一,对天气变化有着显著影响。遥感技术的发展促使土壤湿度的大范围动态性观测变为可能,但对其误差的准确估计仍需进一步的研究。利用ASCAT散射计、AMSR-E辐射计反演得到的2种卫星遥感土壤湿度数据以及ERA-Interim土壤湿度再分析资料,通过三重组合(Triple Collocation,TC)方法得到了研究区域(15°N^55°N,73°E^135°E) 3种土壤湿度数据的误差方差和信噪比估计,并结合MODIS土地覆盖类型数据分析了3种土壤湿度数据的误差特征。结果表明:植被覆盖会影响遥感土壤湿度的TC误差方差估计;从TC误差方差估计值来看,ERA土壤湿度精度最高,AMSR-E精度次之,ASCAT精度最低;从信噪比来看,ASCAT土壤湿度信噪比最高,ERA的信噪比低于ASCAT高于AMSR-E,AMSR-E信噪比最低;通过研究区MODIS土地覆盖类型数据与TC结果的分析可知TC结果多分布在草原、农田和裸地,TC结果比较符合客观实际情况。