Global weak solutions to a spatio-temporal fractional Landau–Lifshitz–Bloch equation

The present paper deals with global existence of weak solutions of a time-space fractional Landau–Lifshitz–Bloch equation involving the weak Caputo derivative and a fractional Laplacian. We use Faedo–Galerkin method with some commutator estimates in order to prove global existence of weak solutions for the model. The uniqueness is also discussed in a special one dimensional case.     

改进ILoG算子的故障检测方法

针对强背景噪声干扰下轮对轴承故障特征微弱、难以准确检测的问题,提出了一种自适应改进高斯拉普拉斯(improved Laplacian of Gaussian,简称ILoG)算子的微弱故障检测方法。ILoG算子滤波器具有优良的信号突变特征检测能力,将其用于轮对轴承故障信号的冲击特征检测,同时利用水循环算法(water cycle algorithm,简称WCA)的寻优特性,并行搜寻筛选最佳的ILoG算子影响参数,通过对参数优化后ILoG算子滤波后信号做进一步包络解调分析,提取出轮对轴承微弱的故障特征信息。对实际轮对轴承外圈和内圈故障信号分析的结果表明,该方法可以有效检测出轴承微弱故障特征频率,故障检测效果优于小波阈值和多尺度形态学差值滤波方法。     

Laplacian regularized robust principal component analysis for process monitoring

Principal component analysis (PCA) is one of the most widely used techniques for process monitoring. However, it is highly sensitive to sparse errors because of the assumption that data only contains an underlying low-rank structure. To improve classical PCA in this regard, a novel Laplacian regularized robust principal component analysis (LRPCA) framework is proposed, where the “robust” comes from the introduction of a sparse term. By taking advantage of the hypergraph Laplacian, LRPCA not only can represent the global low-dimensional structures, but also capture the intrinsic non-linear geometric information. An efficient alternating direction method of multipliers is designed with convergence guarantee. The resulting subproblems either have closed-form solutions or can be solved by fast solvers. Numerical experiments, including a simulation example and the Tennessee Eastman process, are conducted to illustrate the improved process monitoring performance of the proposed LRPCA.     

高碾压混凝土重力坝分区材料-结构界面特性与变形协调仿真分析

高碾压混凝土重力坝不同功能部位"结构特性"与"材料性能"的差异产生的变形协调问题直接关系到工程结构的安全运行,现阶段变形协调分析多是对结构变形和受力进行分析,对异种材料变形协调机理认识不足,缺乏理论基础研究。本文基于界面力学理论,考虑混凝土坝分区中常见的两种双材料界面形式与理想界面的连续边界条件,基于奇异性特征值的特征方程,提出了以应力奇异性特征值作为异种材料变形协调的评价指标,并通过有限元分析验证了理论计算的正确性与有效性;进而分析了界面结合角度和异种材料组合对单侧自由界面端与埋入界面折点处应力奇异性的影响,通过非均质有限元数值仿真分析了复合试件破坏模式,研究了抗压强度与应力奇异性特征值的关系;最后通过统计实际混凝土坝工程中不同坝段内的双材料界面的材料参数(弹性模量)与结构参数(界面形式与结合角度),计算奇异性特征值,评价了该工程中界面的变形协调特性,为高混凝土坝分区材料-结构设计与材料选取提供新的思路。     

Decomposition and replacement: Spatial knowledge distillation for monocular depth estimation

Knowledge distillation has become a key technique for making smart and light-weight networks through model compression and transfer learning. Unlike previous methods that applied knowledge distillation to the classification task, we propose to exploit the decomposition-and-replacement based distillation scheme for depth estimation from a single RGB color image. To do this, Laplacian pyramid-based knowledge distillation is firstly presented in this paper. The key idea of the proposed method is to transfer the rich knowledge of the scene depth, which is well encoded through the teacher network, to the student network in a structured way by decomposing it into the global context and local details. This is fairly desirable for the student network to restore the depth layout more accurately with limited resources. Moreover, we also propose a new guidance concept for knowledge distillation, so-called ReplaceBlock, which replaces blocks randomly selected in the decoded feature of the student network with those of the teacher network. Our ReplaceBlock gives a smoothing effect in learning the feature distribution of the teacher network by considering the spatial contiguity in the feature space. This process is also helpful to clearly restore the depth layout without the significant computational cost. Based on various experimental results on benchmark datasets, the effectiveness of our distillation scheme for monocular depth estimation is demonstrated in details. The code and model are publicly available at : https://github.com/tjqansthd/Lap_Rep_KD_Depth.     

求解代数特征值反问题的RCDE算法

利用向量ε—算法对求解含参数的代数特征值反问题的 CDE 算法作了改进,使其收敛速度由原来的一阶提高到二阶,改进后的 CDE 算法称为 RCDE 算法,数值计算结果表明,RCDE算法确实是一种有效的计算方法。     

非齐次特征值问题

所谓非齐次特征值问题就是给定一个矩阵 A,一个向量 b 及实数 S>0,求数λ工和向量 X使得 AX=λX+b 并且 X~HX=S~2,则称λ为非齐次特征值,相应的向量 X 称为非齐次特征向量。本文介绍产生非齐次特征值的主要背景,讨论非齐次特征值问题解的存在性及解的个数,描述求解非齐次特征值问题的数值方法。     

非齐次对称特征值问题

所谓非齐次对称特征值问题就是给定对称矩阵A,一个向量b,求实数λ和向量X使得AX=λX+b并且‖×‖_2=1,则称λ为非齐次特征值,相应的向量X称为非齐次特征向量、本文讨论了非齐次对称特征值问题解的存在性及解的个数;描述了求解非齐次对称特征值问题的数值方法.     

浅谈某商住小区基础方案的选择

从某市城区一商住开发小区地质勘探入手，通过对场地岩土工程条件、工程造价指标及实际试挖情况进行了分析对比，择优确定了地基基础方案，可供类似工程参考借鉴。