A Dimensional Reduction Approach Based on Essential Constraints in Linear Programming

This paper presents a new dimension reduction strategy for medium and large-scale linear programming problems. The proposed method uses a subset of the original constraints and combines two algorithms: the weighted average and the cosine simplex algorithm. The first approach identifies binding constraints by using the weighted average of each constraint, whereas the second algorithm is based on the cosine similarity between the vector of the objective function and the constraints. These two approaches are complementary, and when used together, they locate the essential subset of initial constraints required for solving medium and large-scale linear programming problems. After reducing the dimension of the linear programming problem using the subset of the essential constraints, the solution method can be chosen from any suitable method for linear programming. The proposed approach was applied to a set of well-known benchmarks as well as more than 2000 random medium and large-scale linear programming problems. The results are promising, indicating that the new approach contributes to the reduction of both the size of the problems and the total number of iterations required. A tree-based classification model also confirmed the need for combining the two approaches. A detailed numerical example, the general numerical results, and the statistical analysis for the decision tree procedure are presented.

Numerical method for dynamics of multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints

Based on the dynamical theory of multi-body systems with nonholonomic constraints and an algorithm for complementarity problems, a numerical method for the multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints is presented. In particular, a wheeled multi-body system is considered. Here, the state transition of stick-slip between wheel and ground is transformed into a nonlinear complementarity problem （NCP）. An iterative algorithm for solving the NCP is then presented using an event-driven method. Dynamical equations of the multi-body system with holonomic and nonholonomic constraints are given using Routh equations and a con- straint stabilization method. Finally, an example is used to test the proposed numerical method. The results show some dynamical behaviors of the wheeled multi-body system and its constraint stabilization effects.

Three-dimensional gravity inversion based on sparse recovery iteration using approximate zero norm

This research proposes a novel three-dimensional gravity inversion based on sparse recovery in compress sensing. Zero norm is selected as the objective function, which is then iteratively solved by the approximate zero norm solution. The inversion approach mainly employs forward modeling; a depth weight function is introduced into the objective function of the zero norms. Sparse inversion results are obtained by the corresponding optimal mathematical method. To achieve the practical geophysical and geological significance of the results, penalty function is applied to constrain the density values. Results obtained by proposed provide clear boundary depth and density contrast distribution information. The method's accuracy, validity, and reliability are verified by comparing its results with those of synthetic models. To further explain its reliability, a practical gravity data is obtained for a region in Texas, USA is applied. Inversion results for this region are compared with those of previous studies, including a research of logging data in the same area. The depth of salt dome obtained by the inversion method is 4.2 km, which is in good agreement with the 4.4 km value from the logging data. From this, the practicality of the inversion method is also validated.

A branch-and-bound algorithm for multi-dimensional quadratic 0-1 knapsack problems

In this paper, a branch-and-bound method for solving multi-dimensional quadratic 0-1 knapsack problems was studied. The method was based on the Lagrangian relaxation and the surrogate constraint technique for finding feasible solutions. The Lagrangian relaxations were solved with the maximum-flow algorithm and the Lagrangian bounds was determined with the outer approximation method. Computational results show the efficiency of the proposed method for multi-dimensional quadratic 0-1 knapsack problems.

Three dimensional K-Tz stress fields around the embedded center elliptical crack front in elastic plates

Through detailed three-dimensional （3D） finite element （FE） calculations, the out-of-plane constraints Tz along embedded center-elliptical cracks in mode I elastic plates are studied. The distributions of Tz are obtained near the crack front with aspect ratios （a/c） of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. Tz decreases from an approximate value of Poisson ratio v at the crack tip to zero with increasing normalized radial distances （r/a） in the normal plane of the crack front line, and increases gradually when the elliptical parameter angle φ changes from 0° to 90°at the same r/a. With a/c rising to 1.0, Tz is getting nearly independent of φ and is only related to r/a. Based on the present FE calculations for Tz, empirical formulas for Tz are obtained to describe the 3D distribution of Tz for embedded center-elliptical cracks using the least squares method in the range of 0.2 ≤ a/c ≤ 1.0. These Tz results together with the corresponding stress intensity factor K are well suitable for the analysis of the 3D embedded centerelliptical crack from field, and a two-parameter K-Tz principle is proposed.

Adaptive Metric Learning for Dimensionality Reduction

Finding a suitable space is one of the most critical problems for dimensionality reduction. Each space corresponds to a distance metric defined on the sample attributes, and thus finding a suitable space can be converted to develop an effective distance metric. Most existing dimensionality reduction methods use a fixed pre-specified distance metric. However, this easy treatment has some limitations in practice due to the fact the pre-specified metric is not going to warranty that the closest samples are the truly similar ones. In this paper, we present an adaptive metric learning method for dimensionality reduction, called AML. The adaptive metric learning model is developed by maximizing the difference of the distances between the data pairs in cannot-links and those in must-links. Different from many existing papers that use the traditional Euclidean distance, we use the more generalized l2,p-norm distance to reduce sensitivity to noise and outliers, which incorporates additional flexibility and adaptability due to the selection of appropriate p-values for different data sets. Moreover, considering traditional metric learning methods usually project samples into a linear subspace, which is overstrict. We extend the basic linear method to a more powerful nonlinear kernel case so that well capturing complex nonlinear relationship between data. To solve our objective, we have derived an efficient iterative algorithm. Extensive experiments for dimensionality reduction are provided to demonstrate the superiority of our method over state-of-the-art approaches.

Three-Dimensional Stress Fields in Finite Thickness Plate with Hole Under Shear Load

The theoretical solutions are obtained for the three-dimensional(3-D)stress field in an infinite isotropic elastic plate with a through-the-thickness circular hole subjected to shear load at far field by using Kane and Mindlin′s assumption based on the stress function method.Based on the present solutions,the characteristics of 3-D stress field are analyzed and the emphasis is placed on the effects of the plate thickness and Poisson′s ratio on the deviation of the present 3-D in-plane stress from the related plane stress solutions,the stress concentration and the out-of-plane constraint.The present solutions show that the stress concentration factor reaches its peak value of about 8.9% which is higher than that of the plane stress solutions.As expected,the out-of-plane stress constraint factor can reach 1on the surface of the hole when the plate is a very thick one.

考虑电力网络约束的工业园区虚拟电厂调控边界求解方法

构建以新能源为主体的新型电力系统,亟须挖掘负荷侧灵活调节资源参与电网调控。含电解铝、矿热炉等高耗能负荷的工业园区具备良好的调控潜力,但是考虑园区内部电力网络约束,其精确调控边界求解面临着变量维数高、约束非线性的难题,现有方法不能较好地兼顾计算效率和精度。对此,文中将上述问题抽象为高维非线性状态空间在P-Q耦合平面的投影问题:分别建立考虑工业园区安全运行线性化和非线性约束的调控边界投影求解模型,采用一种新颖的高维状态空间投影算法,通过顶点“搜索-映射”的两步式求解过程,得到工业园区型虚拟电厂调控边界的精确投影。算例结果表明,采用所提方法求解的调控边界可由线性不等式组完全表征,与现有调度系统完全兼容,结合与叠加柔性资源调控能力和传统采样方法的对比,验证了该方法的可行性以及高求解精度和效率。

基于降维字典学习的高维数据分类策略

为了解决字典学习中的高维数据与非线性问题,提出一种基于降维字典学习的高维数据分类策略。在降维阶段,利用自编码器学习一种非线性映射,该映射可以降维并保留高维数据的非线性结构;在字典学习阶段,利用标签嵌入进行局部约束;在学习过程中,保留了可分解的非线性局部结构,增强了类的区分能力,同时优化了映射函数和字典。在多个基准数据集上的实验结果表明,提出的方法能够有效解决字典学习中的高维数据与非线性问题。

环境约束视角下集合住宅邻里交往空间在垂直维度的重构与进化

目前国内大规模建设的集合住宅与传统住宅比较,普遍存在邻里关系活跃度较低及邻里交往空间有效性不足的问题。因为环境约束条件的变化,传统邻里交往行为的多样性、有机性、心理自由等积极特征在集合住宅中遭到极大的削弱。通过重新建构集合住宅的环境约束条件,在垂直维度上实现多线程交通、开放边界、增加空间冗余度与节点自由度,可以提升邻里交往空间设计的自由度,形成邻里交往空间的自然进化,实现恢复住区内良好邻里关系的目标。

基于互质极化敏感阵列的参数降维估计算法

针对互质极化敏感阵列波达方向角(DOA)和极化参数估计中存在的计算复杂度高以及多信源情况下DOA解模糊配对错误问题,本文提出了一种基于模值约束降维求根多重信号分类(MUSIC)的DOA和极化参数联合估计算法。首先通过重构三维谱函数,对DOA和极化参数进行解耦,实现三维MUSIC方法的降维,然后利用多项式求根求解出DOA,并利用波束形成方法解决了互质阵列中存在的解模糊角度错配问题,最后利用极化矢量的模值有界性构造代价函数,推导出极化参数的闭式解。数值仿真结果验证了所提算法的有效性,结果表明,所提算法参数估计精度高于旋转不变技术(ESPRIT),与一维全局谱峰搜索MUSIC(1D-TSS-MUSIC)算法基本相当,但本文算法显著降低了计算复杂度,且在多信源情况下依然可以获得可靠的参数估计。

基于空间约束联合字典学习的三维冲击波超压场重建

针对有限测点条件下冲击波超压场全时空全区域重建的需求,提出一种基于空间约束联合字典学习的三维冲击波超压场重建方法。建立三维走时层析成像模型,利用字典学习对图像的稀疏表征优势和空间约束对图像边缘纹理保真特性,采用交替最小化思想对目标函数进行优化解算,实现大型病态稀疏矩阵的高精度求解。试验结果表明,该方法与代数重建算法(ART)、联合代数重建算法(SART)和期望极大化算法(EM)相比,重建精度更高,全区域重建误差达到了15.81%,在时空场重建过程中具有较高的应用价值。

混合多类型储能的分布式能源系统运行优化方法

对于含多类型混合储能系统的运行优化,通常将所有设备等效为一个整体,并未考虑各储能系统的运行特性差异等因素,最终导致设备利用率低,经济运行能力差。为此,首先以最大可再生能源消纳以及最小电网交换电量为目标,构建了优化函数模型。其次,考虑到多类型储能系统在充放电动态特性、运行成本特征以及SOC设定等方面差异,提出了一种结合能量型储能SOC一致性约束的双层解耦式运行优化方法,以适应分布式能源系统中的多类型储能协同运行。最后,以某个在建的分布式可再生能源系统工业示范园区数据为基础,对所提方法进行了算例验证与分析。结果证明,所提方法在保证分布式能源系统内多个能量型储能系统充放电同步性的同时,能够对具有相同运行特性的储能系统进行聚类,有效了降低计算复杂性,完成多类型储能协调与优化,并最终促进分布式能源系统的新能源消纳。

测量路面三维纹理的激光约束双目鲁棒算法

为提升激光约束双目重构算法测量路面三维纹理的普适性,增强算法的抗光干扰能力,解决激光约束目标在变化光照下的鲁棒提取问题,基于Faster-RCNN(faster-region based convolutional neural network)构建激光约束识别模型,提取5~1050 lux光照范围内人为构造的激光约束目标,对待测路面的约束目标开展子区域分割,进而实现子区域分割立体匹配下双目三维重构。结果表明:改进算法在1050 lux光照强度下的平均构造深度测量值与铺砂法的拟合系数为0.987,优于原激光约束双目重构算法的0.887;在5~1050 lux光照范围内,改进算法最大波动误差、平均波动误差分别为0.141、0.084 mm,较原激光约束双目重构算法分别降低70.20%和76.83%。

铁路工程装配式三维数字化设计方法研究

为解决铁路工程复杂结构形式下设计建模工作量大、建模精度不高、现有三维设计软件适用性弱等问题,建立构件数据存储标准,基于工程装配式思路,将单个构件作为设计单元进行参数化预设计,实现参数与模型的实时交互;将空间几何线抽象为设计参数并定义为线状约束,约束构件位置和形态,实现构件的精细化设计和组装;建立构件属性与工程量计算模板的映射关系,将构件参数导入模板,快速计算工程量;采用剖切构件几何轮廓线的方式生成二维图。该研究降低了铁路工程复杂单体构件精细化设计的难度,有效提升了复杂结构物建模和修改的效率。

带角度约束的三维积分二阶滑模拦截制导律

针对导弹在三维场景中以期望角度拦截加速度未知的机动目标问题,提出了一种考虑角度约束的三维拦截制导律。首先,建立了三维弹目非线性拦截制导模型;其次,设计了一种全滑动模态的积分滑模面,省去了传统滑模制导律中的滑模趋近阶段,有效地降低了拦截制导过程中的能量消耗;而后,基于设计的积分滑模面和二阶滑模控制理论,在弹目视线法向和侧向上分别设计了一种带角度约束的三维积分二阶滑模拦截制导律,有效地抑制了抖振现象,同时对目标机动造成的未知干扰进行了在线补偿;此外,对所设计算法进行了严格的Lyapunov稳定性数学证明;最后,数值仿真结果验证了本文所提三维拦截制导律的有效性、优越性以及抗干扰的鲁棒性。

基于三维坐标系的动车组运检计划算法模型

构建以动车组-交路\修程-天数三维坐标系数学模型,全面考虑动车组运用与检修计划编制的优化目标和约束条件,构建动车组运检计划优化编制的数学优化模型。在给定动车组数量、交路计划的前提下,根据动车所实际情况,以“天”为最小的计划编制时间单位,通过控制换车次数,以检修时剩余里程为追求目标,阐述并规范运检计划算法实现流程,实现大空间分段式快速粒子群优化算法完成动车组运检计划的快速给定。

面向室内场景的改进MSCKF视觉-惯性里程计算法

搭载高帧率传感器的载体在室内快速运动时,其使用的视觉惯性里程计(VIO)算法存在计算负载高和定位精度下降等问题。针对此问题提出一种面向室内场景的改进多状态约束卡尔曼滤波器的VIO算法。首先,基于梯度和特征值对特征点检测结果进行约束,提高特征点的提取质量进而提升算法的位姿估计精度;然后,使用一维逆深度参数化地图点进行状态增广,降低算法的计算复杂度以提高系统处理速度;最后,分别在公开数据集EuRoC与真实场景下进行了实验,从算法的轨迹估计精度、处理时间以及CPU使用占比率方面对所提算法进行了全面评估。实验结果表明,相较于S-MSCKF、VINS-Mono和PL-VIO三种主流VIO方法,所提算法的定位精度至少提升了19.18%,在确保精度的同时拥有较低的处理时间和CPU占有率,保证了系统的实时性。

Bargmann Symmetry Constraint and Binary Nonlinearization of Super NLS-MKdV Hierarchy

An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of the super NLS-MKdV hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold R4N|2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.

DIMENSION VARIATION OF FEATURE-BASED MODEL BY OPERATING DIRECTLY ON B-REP

ＤＩＭＥＮＳＩＯＮＶＡＲＩＡＴＩＯＮＯＦＦＥＡＴＵＲＥ┐ＢＡＳＥＤＭＯＤＥＬＢＹＯＰＥＲＡＴＩＮＧＤＩＲＥＣＴＬＹＯＮＢ┐ＲＥＰＨＥＸｉａｏｚｈａｏ（何小朝），ＷＡＮＧＺｏｎｇｙａｎ（王宗彦）ＰＥＮＧＷｅｉ（彭维），ＺＨＡＮＧＴｉｅｃｈａｎｇ（张铁昌...