Clarkson-Kruskal Direct Similarity Approach for Differential-Difference Equations

In this letter, the Clarkson-Kruskal direct method is extended to similarity reduce some differentialdifference equations. As examples, the differential-difference KZ equation and KP equation are considered.

THE REGULARITY OF RANDOM GRAPH DIRECTED SELF-SIMILAR SETS

A set in Rd is called regular if its Hausdorff dimension coincides with its upper box counting dimension. It is proved that a random graph-directed self-similar set is regular a.e..

Measurement of Similarity for Spatial Directions Between Areal Objects

Similarity for spatial directions plays an important role in GIS. In this paper, the conventional approaches are analyzed. Based on raster data areal objects, the authors propose two new methods for measuring similarity among spatial directions. One is to measure the similarity among spatial directions based on the features of raster data and the changes of distances between spatial objects, the other is to measure the similarity among spatial directions according to the variation of each raster cell centroid angle. The two methods overcome the complexity of measuring similarity among spatial directions with direction matrix model and solve the limitation of small changes in direction. The two methods are simple and have broader applicability.

基于有向图的城市交叉口场景相似性评价方法

准确的场景相似性评估对于优化测试场景集极为重要。然而,现有的基于轨迹的评价方法未能充分捕捉城市交叉口中车辆间的复杂动态交互特征,从而影响评价结果的准确性。针对此问题,本研究提出了一种基于有向图的城市交叉口场景相似性评价方法,该方法通过比较两个场景中车辆的全局交互拓扑关系在时空上的匹配程度来量化场景之间的相似性。首先,使用有向图来表征各个交叉口中车辆间的交互拓扑结构。然后,通过比较不同交叉口场景的有向图结构匹配程度来估计它们之间的交互相似性。最后,采用动态时间扭曲算法在时间维度上对齐场景,实现两个不同长度测试场景序列的有效比较。3对典型评价案例的定性分析结果显示,该方法能够细粒度地区分不同相似度水平的场景。进一步地,为定量验证方法的有效性,开展了场景相似度与自动驾驶系统性能之间的方差分析实验。实验结果表明,在不同相似度水平场景簇的测试条件下,系统的安全性和效率均表现出显著的差异,从而证实了该方法的有效性。最终,该方法应用于Apollo的测试场景集的优化,结果表明方法能够有效指导测试场景集中同质化场景的剔除,从而提高测试效率。

Conditional Similarity Solutions of the Boussinesq Equation

The direct method proposed by Clarkson and Kruskal is modified to obtain some conditional similarity solutions of a nonlinear physics model. Taking the -dimensional Boussinesq equation as a simple example, six types of conditional similarity reductions are obtained.

Conditional Similarity Reductions of Jimbo—Miwa Equation via the Classical Lie Group Approach

Recently, the Clarkson and Kruskal direct method has been modified to find new similarity reductions (conditional similarity reductions) of nonlinear systems and the results obtained by the modified direct method cannot be obtained by the current classical and/or non-classical Lie group approach. In this paper, we show that the conditional similarity reductions of the Jimbo-Miwa equation can be reobtained by adding an additional constraint equation to the original model to form a conditional equation system first and then solving the model system by means of the classical Lie group approach.

SIMILARITY REDUCTIONS FOR 2+1-DIMENSIONAL VARIABLE COEFFICIENT GENERALIZED KADOMTSEV-PETVIASHVILI EQUATION

With the aid of MATHEMATICA, the direct reduction method,vas extended and applied in 2 + 1-dimensional variable coefficient generalized Kadomtsev-Petviashvili equation( VCGRPE). As a result, several kinds of similarity reductions for VCGKPE are obtained which contain Painleve I, Painleve II and Painleve ni reductions.

Similarity Reductions of(2+1)-Dimensional Multi-component Broer-Kaup System

Painleve property of the （2＋1）-dimensional multi-component Broer-Kaup （BK） system is considered by using the standard Weiss Kruskal approaches. Applying the Clarkson and Kruskal （CK） direct method to the （2＋1）- dimensional multi-component BK system, some types of similarity reductions are obtained. By solving the reductions, one can get the solutions of the （2＋1）-dimensional multi-component BK system.

Shape Similarity Measures of Linear Entities

The essential of feature matching technology lies in how to measure the similarity of spatial entities.Among all the possible similarity measures,the shape similarity measure is one of the most important measures because it is easy to collect the necessary parameters and it is also well matched with the human intuition.In this paper a new shape similarity measure of linear entities based on the differences of direction change along each line is presented and its effectiveness is illustrated.

Conditional Similarity Solutions of （2＋1）—Dimensional General nonintegrable KdV Equation

The real physics models are usually quite complex with some arbitrary parameters which will lead to the nonintegrability of the model. To find some exact solutions of a nonintegrable model with some arbitrary parameters is much more difficult than to find the solutions of a model with some special parameters. In this paper, we make a modification for the usual direct method to find some conditional similarity solutions of a (2+1)-dimensional general nonintegrable KdV equation.

Similarity Reductions of Nonisospectral BKP Equation

Basing on the direct method developed by Clarkson and Kruskal,the nonisospectral BKP equation can bereduced to three types of(1+1)-dimensional variable coefficients partial differential equations(PDEs).Furthermore,onthe basis of the idea of the symmetry group direct method by Lou et al.,three types of reduction PDEs are all reducedto the related constant coefficients PDEs by some transformations.

Similarity Reductions of Nearly Concentric KdV Equation

Basing on the direct method developed by Clarkson and Kruskal, the nearly concentric Korteweg-de Vries （ncKdV） equation can be reduced to three types of （1＋1）-dimensional variable coefficients partial differential equations （PDEs） and three types of variable coefficients ordinary differential equation. Furthermore, three types of （1＋1）-dimensional variable coefficients PDEs are all reduced to constant coefficients PDEs by some transformations.

基于三维空间面积划分的轨迹相似性度量算法

针对大部分轨迹相似性度量算法无法区分方向相反轨迹的问题,提出了一种基于三维空间面积划分的三维三角分割(3TD)算法。首先,按照3TD算法的时间转换规则将轨迹集的绝对时间序列转变为相对时间序列;然后,在由经度、纬度以及时间三要素构成的三维空间坐标系中,通过划分规则将轨迹间面积分割成若干互不重叠的三角形,累加三角形面积并计算轨迹相似度;最后,在从船舶自动识别系统(AIS)收集的随机采样轨迹数据集上,与最长公共子序列(LCSS)算法和三角分割(TD)算法等进行了对比实验。实验结果表明:3TD算法对实验数据集中异向轨迹识别精确度达到100%;同时该算法面对海量数据集以及轨迹点部分缺失的数据集时,也能维持准确的度量结果以及较高的运算效率,能更好地适应异向轨迹相似度量工作。

立轴双向泵装置压力脉动特性相似律

压力脉动特性是影响立轴双向泵装置运行稳定性的主要因素之一,因此针对该泵装置开展原型和模型压力脉动特性相似性研究非常必要。以某立轴双向泵站为例,采用非定常三维模拟方法对模型泵装置和原型泵装置关键位置的压力脉动特性进行预测,并在模型试验装置和原型泵装置中测量相应测点和工况下的压力脉动幅值,分析原型和模型泵装置压力脉动之间的相似关系。结果表明:泵装置压力脉动幅值与外特性之间存在一定的关联性;模型泵装置试验测试脉动信号的频谱比原型泵装置丰富得多,但两者在3、6、9倍转频处均存在压力脉动峰值,在这些频率处的压力脉动表现出很好的相似性;原型和模型压力脉动数值模拟结果完全相似,主频下原型实测幅值与模型实测幅值误差在3%左右,与模拟预测值幅值的误差约为16%,均为偏安全,能够满足工程设计要求。

基于复域暂态解析的柔性直流输电线路单端故障测距方法

输电线路的精确故障测距能降低巡线的难度、缩短修复时间,提升柔性直流输电线路单端故障测距方法的精度具有重要意义。文中基于故障时域暂态波形相似度特征模型,以柔性直流输电系统复域故障暂态解析计算模型作为特征拟合工具,通过故障录波与解析结果的波形相似性评价特征拟合程度,将故障测距问题转化为余弦相似度、平均绝对差两个评估指标的优化问题进行求解;提出了基于复域暂态解析拟合的柔性直流输电线路故障测距方法。最后,通过PSCAD/EMTDC仿真验证了所提故障测距方法的有效性。所提方法耐受过渡电阻能力强,无须依赖大量仿真与训练来提高测距精度。

煤层群叠加开采覆岩裂隙演化及卸压瓦斯抽采研究

针对采动裂隙带卸压瓦斯抽采效果不佳导致的工作面上隅角瓦斯超限的问题。以赵家寨煤矿11210工作面为工程背景,采用物理相似模拟实验方法,研究了煤层群叠加开采对上覆岩层采动裂隙的演化特征,并通过现场验证确定了瓦斯抽采的最优层位。结果表明:煤层群叠加开采过程中,在卸压区域外,形成了较大的应力集中,在卸压保护范围内,应力集中现象不明显,且应力峰值小于二1煤层原始应力;煤层群叠加开采引起了采场上覆岩层的叠加卸压,使上覆岩层的位移场发生了叠加变化,岩层最大下沉量进一步增加;煤层群叠加开采结束后,采空区上覆岩层中部岩层被压实,两端岩层裂隙较为发育,形成了一定范围的裂隙发育区。通过现场试验,确定了裂隙带定向长钻孔合理层位的选择,并在现场进行钻孔监测,验证了物理相似模拟结果的合理性。

基于格网锥形方向的关系模型计算方向相似性研究

针对方向关系矩阵在定量计算空间对象方向相似关系方面存在的表达能力、多尺度地图数据下应用能力不足的问题,提出一种格网锥形方向关系模型,完成对空间对象方向关系的定量表达。对同尺度下格网锥形方向关系模型的表达能力进行试验分析,并对不同尺度下格网锥形方向关系模型的应用能力进行分析,分析对比后验证了本文方法可行,空间方向相似性度量结果和人们的认知结果一致,可应用于制图综合、空间数据查询更新、空间数据变化检测等任务。

基于并行小波算法的多模态数据近似匹配模型构建

针对近似匹配过程易受数据冗余性、异构成分等的影响,提出了基于并行小波算法的多模态数据近似匹配模型。该模型首先采用并行小波算法剔除多模态数据中的噪声,避免噪声对匹配过程产生影响;其次采用张量分解的聚类算法将不同相似度的数据划分到不同类簇中,以消除不同类簇的数据差异度;最后将预处理后的数据输入到基于空间方向近似性的数据匹配模型中,通过计算参考数据与待匹配数据之间的空间方向近似度、编辑距离完成多模态数据的近似匹配。实验结果表明,所提方法的匹配查准率高、查全率高、匹配时间短。

近距离煤层采空区下开采底板破坏规律研究

为研究近距离煤层上层煤采空区对下层煤采动底板破坏的影响,以塔山矿8199工作面为例,通过统计公式和塑性力学公式预计工作面底板破坏深度;采用双向加载相似模拟试验分析顶板有无采空区对底板破坏的影响;利用“专门电极电缆直流电法”现场观测采动过程中底板视电阻率变化,获得底板最大破坏深度。结果表明:8#煤底板破坏深度受顶板采空区和底板岩性组合的双重影响;顶板采空区的存在使8#煤开采时底板初始应力减小,应力集中程度减弱,回采过程中直接顶垮落步距减小,易形成“短砌体梁”结构,顶板周期来压伴随着底板裂隙的扩展;工作面底板实测最大破坏深度17.1 m,相比于统计公式和塑性力学公式,预测值分别减小11.4%和7.8%,塑性力学公式相对适用性更好。

基于栅格数据的面状目标空间方向相似性研究

提出了基于栅格数据的面状目标之间的两种空间方向相似性的计算方法 :利用栅格数据的特征和方向关系矩阵计算空间方向相似性 ;基于单个栅格单元与参考目标之间角度的变化计算面状目标之间空间方向相似性。这两种方法简化了由Goyal提出的基于方向关系矩阵模型计算空间方向相似性的方法 ,克服了方向产生某些细微变化时的限制 。