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判断并解决线性规划“多反而少”悖论的逆最优值解法
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作者 杨德权 王佳 《运筹与管理》 CSSCI CSCD 北大核心 2015年第1期75-80,共6页
现有研究通过调整线性规划模型的右端项来消除"多反而少"悖论,而该文提出并验证了悖论是由技术系数矩阵、目标函数系数以及右端项三者的不合理搭配造成的。首先,通过建立原-对偶模型来判断悖论现象存在与否;然后,将悖论问题... 现有研究通过调整线性规划模型的右端项来消除"多反而少"悖论,而该文提出并验证了悖论是由技术系数矩阵、目标函数系数以及右端项三者的不合理搭配造成的。首先,通过建立原-对偶模型来判断悖论现象存在与否;然后,将悖论问题转换成逆最优值问题进行解决,构建了通过调整目标函数系数以及技术系数矩阵来消除悖论的模型;最后,提出了判断并解决悖论的逆最优值解法,阐述了其优势与经济意义,并通过数值算例验证其有效性。 展开更多
关键词 运筹学 原-对偶模型 逆最优值解法 “多反而少”悖论
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Euler方程的多网格数值解法
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作者 周新海 周新国 《计算机工程与科学》 CSCD 1989年第2期36-43,共8页
本文提出一种求解Euler方程的多网格算法,对于亚音速、跨音速叶栅绕流计算具有显著加速收敛的效果。叙述了方法的基本原理和在不同尺寸的网格间变量的传递、分配和回插过程。用多网格法进行多种叶栅绕流的对比计算,证明了方法的有效性。
关键词 叶栅 叶型 值解法 网格法 EULER方程 网格数 基本格式 跨音速流 网格点 加速效果
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适用于“银河”机上几种非线性方程组的数值解法
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作者 陈杏伦 《计算机工程与科学》 CSCD 1990年第4期75-82,共8页
一、引言非线性方程组的一般形式: f(x)=0 x∈(?)R<sup>n</sup> (A) 其中f(x)=(f<sub>1</sub>(x),f<sub>2</sub>(x),…,f<sub>n</sub>(x))<sup>T</sup>,x... 一、引言非线性方程组的一般形式: f(x)=0 x∈(?)R<sup>n</sup> (A) 其中f(x)=(f<sub>1</sub>(x),f<sub>2</sub>(x),…,f<sub>n</sub>(x))<sup>T</sup>,x=(x<sub>1</sub>,x<sub>2</sub>,…,x<sub>n</sub>)<sup>T</sup>。即f(x)是以f<sub>i</sub>(x)为分量的向量函数。当n=1时,就是只含一个未知量的非线性方程。我们的目的是求向量x<sup>*</sup>=(x<sub>1</sub><sup>*</sup>,x<sub>2</sub><sup>*</sup>,…,x<sub>n</sub><sup>*</sup>)<sup>T</sup>,使其满足f(x<sup>*</sup>)=0,称此x<sup>*</sup>为(A)的解。除少数的特殊方程组外,直接解法几乎是不可能的。常用的有效数值解法一般都采用迭代法。在迭代法中最基本而重要的是Newton迭代法,因一些很有成效的算法,都是在它的基础上发展而成的。虽然牛顿法具有收敛速度快(二阶收敛)。 展开更多
关键词 非线性方程组 迭代法 二阶收敛 牛顿法 直接解法 值解法 向量函数 JACOBI 收敛性定理
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图解法和矩值法粒度参数的定性对比:以琼州海峡岸滩表层沉积物为例 被引量:2
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作者 李高聪 梁荣鑫 +4 位作者 仝长亮 王华强 夏琼 李志强 唐杰平 《海洋学报》 CAS CSCD 北大核心 2023年第2期98-109,共12页
前人已开展了大量的关于图解法和矩值法数值结果的相关性分析和相互转换方程的确定工作,但针对定性结果的对比仍较为罕见。本文选取了琼州海峡两岸15个海滩22条断面105个表层沉积物为典型研究对象,分别采用Folk和Ward图解法和Friedman... 前人已开展了大量的关于图解法和矩值法数值结果的相关性分析和相互转换方程的确定工作,但针对定性结果的对比仍较为罕见。本文选取了琼州海峡两岸15个海滩22条断面105个表层沉积物为典型研究对象,分别采用Folk和Ward图解法和Friedman矩值法获取粒度参数结果,构建定量结果的回归关系和对比定性结果的异同。结合前人的研究成果,本文进一步探讨了两种方法结果的可对比性,并分析两种方法的方法差异对沉积物粒度信息提取及使用造成的可能影响。研究结果表明:(1)就定量结果而言,图解法和矩值法计算的平均粒径和分选系数具有强相关性(R2≥0.951),而偏态和峰态则表现为中等相关(R2=0.586)和不相关(R2=0.011),表明图解法和矩值法计算粒度参数定量结果之间的相关性并不稳定,这与前人的研究结果基本一致;(2)就定性结果而言,图解法和矩值法的结果之间存在较大偏差,分选系数、偏态和峰态不一致的占比分别达30.48%、55.24%和71.43%,这与定量结果的相关性存在一定程度的偏差,表明定量结果的相关性程度并不能完全用于指示定性术语结果的一致性程度。鉴于最大化地揭示沉积物的差异是粒度参数分析方法追寻的目标,在选择何种方法计算粒度参数时需充分考虑沉积物粒径概率分布曲线的特征。本文提供了一个以海滩沉积物为研究对象的图解法和矩值法粒度参数结果对比的典型案例,研究结果有助于提升对粒度参数分析方法的差异、原因和科学使用等方面的认识。 展开更多
关键词 粒度参数 海滩沉积物 解法和矩 定量和定性对比 琼州海峡两岸
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移动车载识别的两种解法及其试验验证 被引量:2
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作者 余岭 陈鸿天 罗绍湘 《长江科学院院报》 CSCD 北大核心 2001年第5期84-87,共4页
大多数移动车载识别方法最终转化为线性方程组 ,其不同的求解方法往往给出不同的识别精度。利用频时域法由桥梁响应识别桥面移动车载 ,重点比较了伪逆解法和奇异值解法的识别结果 ,并讨论了几个主要参数对识别结果的影响。结果表明 ,使... 大多数移动车载识别方法最终转化为线性方程组 ,其不同的求解方法往往给出不同的识别精度。利用频时域法由桥梁响应识别桥面移动车载 ,重点比较了伪逆解法和奇异值解法的识别结果 ,并讨论了几个主要参数对识别结果的影响。结果表明 ,使用奇异值解法能够明显提高频时域法的识别精度。 展开更多
关键词 车桥相互作用 移动荷载识别 频时域法 奇异值解法 伪逆解法 桥面移动车载 桥梁响应 车辆轮载 间接识别
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柔性薄壁大部件数字化装配调姿算法研究 被引量:4
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作者 李树军 罗浩 +2 位作者 庞放心 赵伟 封璞加 《航空制造技术》 2019年第8期38-43,共6页
采用定位器托架混合调姿定位平台,提出了一种飞机薄壁柔性大部件数字化调姿方法。首先,采用奇异值分解法(SVD)计算机翼位姿,通过运动学逆解得到定位器各轴的运动状态。其次,根据飞机大部件易变形的特点,提出了一种消除位姿计算误差的建... 采用定位器托架混合调姿定位平台,提出了一种飞机薄壁柔性大部件数字化调姿方法。首先,采用奇异值分解法(SVD)计算机翼位姿,通过运动学逆解得到定位器各轴的运动状态。其次,根据飞机大部件易变形的特点,提出了一种消除位姿计算误差的建立飞机部件坐标系的方法,实现快速高精度调姿。最后,将该方法应用于飞机机翼的调姿,经测量调姿精度满足装配要求。 展开更多
关键词 柔性大部件 数字化装配 奇异解法(SVD) 调姿 定位器
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Super-resolution reconstruction of synthetic-aperture radar image using adaptive-threshold singular value decomposition technique 被引量:2
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作者 朱正为 周建江 《Journal of Central South University》 SCIE EI CAS 2011年第3期809-815,共7页
A super-resolution reconstruction approach of (SVD) technique was presented, and its performance was radar image using an adaptive-threshold singular value decomposition analyzed, compared and assessed detailedly. F... A super-resolution reconstruction approach of (SVD) technique was presented, and its performance was radar image using an adaptive-threshold singular value decomposition analyzed, compared and assessed detailedly. First, radar imaging model and super-resolution reconstruction mechanism were outlined. Then, the adaptive-threshold SVD super-resolution algorithm, and its two key aspects, namely the determination method of point spread function (PSF) matrix T and the selection scheme of singular value threshold, were presented. Finally, the super-resolution algorithm was demonstrated successfully using the measured synthetic-aperture radar (SAR) images, and a Monte Carlo assessment was carried out to evaluate the performance of the algorithm by using the input/output signal-to-noise ratio (SNR). Five versions of SVD algorithms, namely 1 ) using all singular values, 2) using the top 80% singular values, 3) using the top 50% singular values, 4) using the top 20% singular values and 5) using singular values s such that S2≥/max(s2)/rinsNR were tested. The experimental results indicate that when the singular value threshold is set as Smax/(rinSNR)1/2, the super-resolution algorithm provides a good compromise between too much noise and too much bias and has good reconstruction results. 展开更多
关键词 synthetic-aperture radar image reconstruction SUPER-RESOLUTION singular value decomposition adaptive-threshold
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Wavelet matrix transform for time-series similarity measurement 被引量:2
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作者 胡志坤 徐飞 +1 位作者 桂卫华 阳春华 《Journal of Central South University》 SCIE EI CAS 2009年第5期802-806,共5页
A time-series similarity measurement method based on wavelet and matrix transform was proposed,and its anti-noise ability,sensitivity and accuracy were discussed. The time-series sequences were compressed into wavelet... A time-series similarity measurement method based on wavelet and matrix transform was proposed,and its anti-noise ability,sensitivity and accuracy were discussed. The time-series sequences were compressed into wavelet subspace,and sample feature vector and orthogonal basics of sample time-series sequences were obtained by K-L transform. Then the inner product transform was carried out to project analyzed time-series sequence into orthogonal basics to gain analyzed feature vectors. The similarity was calculated between sample feature vector and analyzed feature vector by the Euclid distance. Taking fault wave of power electronic devices for example,the experimental results show that the proposed method has low dimension of feature vector,the anti-noise ability of proposed method is 30 times as large as that of plain wavelet method,the sensitivity of proposed method is 1/3 as large as that of plain wavelet method,and the accuracy of proposed method is higher than that of the wavelet singular value decomposition method. The proposed method can be applied in similarity matching and indexing for lager time series databases. 展开更多
关键词 wavelet transform singular value decomposition inner product transform time-series similarity
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Effects of different numerical algorithms on simulation of chemical dissolution-front instability in fluid-saturated porous rocks 被引量:3
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作者 ZHAO Chong-bin Bruce HOBBS Alison ORD 《Journal of Central South University》 SCIE EI CAS CSCD 2018年第8期1966-1975,共10页
Many scientific and engineering problems need to use numerical methods and algorithms to obtain computational simulation results because analytical solutions are seldom available for them.The chemical dissolution-fron... Many scientific and engineering problems need to use numerical methods and algorithms to obtain computational simulation results because analytical solutions are seldom available for them.The chemical dissolution-front instability problem in fluid-saturated porous rocks is no exception.Since this kind of instability problem has both the conventional(i.e.trivial)and the unconventional(i.e.nontrivial)solutions,it is necessary to examine the effects of different numerical algorithms,which are used to solve chemical dissolution-front instability problems in fluid-saturated porous rocks.Toward this goal,two different numerical algorithms associated with the commonly-used finite element method are considered in this paper.In the first numerical algorithm,the porosity,pore-fluid pressure and acid/solute concentration are selected as basic variables,while in the second numerical algorithm,the porosity,velocity of pore-fluid flow and acid/solute concentration are selected as basic variables.The particular attention is paid to the effects of these two numerical algorithms on the computational simulation results of unstable chemical dissolution-front propagation in fluid-saturated porous rocks.The related computational simulation results have demonstrated that:1)the first numerical algorithm associated with the porosity-pressure-concentration approach can realistically simulate the evolution processes of unstable chemical dissolution-front propagation in chemical dissolution systems.2)The second numerical algorithm associated with the porosity-velocity-concentration approach fails to simulate the evolution processes of unstable chemical dissolution-front propagation.3)The extra differential operation is the main source to result in the failure of the second numerical algorithm. 展开更多
关键词 numerical algorithm chemical dissolution front instability computational simulation porous rocks
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Impulsive component extraction using shift-invariant dictionary learning and its application to gear-box bearing early fault diagnosis 被引量:4
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作者 ZHANG Zhao-heng DING Jian-ming +1 位作者 WU Chao LIN Jian-hui 《Journal of Central South University》 SCIE EI CAS CSCD 2019年第4期824-838,共15页
The impulsive components induced by bearing faults are key features for assessing gear-box bearing faults.However,because of heavy background noise and the interferences of other vibrations,it is difficult to extract ... The impulsive components induced by bearing faults are key features for assessing gear-box bearing faults.However,because of heavy background noise and the interferences of other vibrations,it is difficult to extract these impulsive components caused by faults,particularly early faults,from the measured vibration signals.To capture the high-level structure of impulsive components embedded in measured vibration signals,a dictionary learning method called shift-invariant K-means singular value decomposition(SI-K-SVD)dictionary learning is used to detect the early faults of gear-box bearings.Although SI-K-SVD is more flexible and adaptable than existing methods,the improper selection of two SI-K-SVD-related parameters,namely,the number of iterations and the pattern lengths,has an adverse influence on fault detection performance.Therefore,the sparsity of the envelope spectrum(SES)and the kurtosis of the envelope spectrum(KES)are used to select these two key parameters,respectively.SI-K-SVD with the two selected optimal parameter values,referred to as optimal parameter SI-K-SVD(OP-SI-K-SVD),is proposed to detect gear-box bearing faults.The proposed method is verified by both simulations and an experiment.Compared to the state-of-the-art methods,namely,empirical model decomposition,wavelet transform and K-SVD,OP-SI-K-SVD has better performance in diagnosing the early faults of a gear-box bearing. 展开更多
关键词 gear-box bearing fault diagnosis shift-invariant K-means singular value decomposition impulsive component extraction
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Numerical modeling dynamic process of multi-feed microwave heating of industrial solution media 被引量:5
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作者 杨彪 孙俊 +7 位作者 李玮 彭金辉 李幼灵 罗会龙 郭胜惠 张竹敏 苏鹤州 史亚鸣 《Journal of Central South University》 SCIE EI CAS CSCD 2016年第12期3192-3203,共12页
The exothermic efficiency of microwave heating an electrolyte/water solution is remarkably high due to the dielectric heating by orientation polarization of water and resistance heating by the Joule process occurred s... The exothermic efficiency of microwave heating an electrolyte/water solution is remarkably high due to the dielectric heating by orientation polarization of water and resistance heating by the Joule process occurred simultaneously compared with pure water.A three-dimensional finite element numerical model of multi-feed microwave heating industrial liquids continuously flowing in a meter-scale circular tube is presented.The temperature field inside the applicator tube in the cavity is solved by COMSOL Multiphysics and professional programming to describe the momentum,energy and Maxwell's equations.The evaluations of the electromagnetic field,the temperature distribution and the velocity field are simulated for the fluids dynamically heated by singleand multi-feed microwave system,respectively.Both the pilot experimental investigations and numerical results of microwave with single-feed heating for fluids with different effective permittivity and flow rates show that the presented numerical modeling makes it possible to analyze dynamic process of multi-feed microwave heating the industrial liquid.The study aids in enhancing the understanding and optimizing of dynamic process in the use of multi-feed microwave heating industrial continuous flow for a variety of material properties and technical parameters. 展开更多
关键词 microwave with multi-feed heating industrial flow dynamical process numerical computation solution media
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Comparison of structure and physical fields in 400 kA aluminum reduction cells 被引量:1
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作者 丁吉林 李劼 +3 位作者 张红亮 徐宇杰 杨帅 刘业翔 《Journal of Central South University》 SCIE EI CAS 2014年第11期4097-4103,共7页
To investigate the differences and the development trends of the 400 kA aluminum reduction cell, four representative cells were deeply analyzed. By using numerical simulation methods in ANSYS software, the structure p... To investigate the differences and the development trends of the 400 kA aluminum reduction cell, four representative cells were deeply analyzed. By using numerical simulation methods in ANSYS software, the structure parameters were firstly compared, and then three-dimensional models of electric-magnetic-flow field were built and solved with finite element method(FEM). The comparison of the structures reveals that the cell bodies are similar while the current flow path and distribution ratio of bus bars are different. It appears that most of the current(70%-80%) in side A are used as the magnetic field compensation current and flow through two ends. The numerical simulation results indicate that the distributions of magnetic fields are different but all satisfy with the magnetohydrodynamics(MHD) stabilization, and the flow patterns are all two or multi vortexes with appropriate velocities. The comparison shows that all studied cells can satisfy with the physical field requirement, and the commercial applications also verify that the 400 kA cells have become the product of the mature and world's leading technology. 展开更多
关键词 aluminum electrolysis numerical simulation bus structure physical field
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